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The post-processing of quantum key distribution mainly includes error correction and privacy amplification. The error correction algorithms and privacy amplification methods used in the existing quantum key distribution are completely unrelated. Based on the principle of correspondence between error-correcting codes and hash function families, we proposed the idea of time-division multiplexing for error correction and privacy amplification for the first time. That is to say, through the common error correction algorithms and their corresponding hash function families or the common hash function families and their corresponding error-correcting codes, error correction and privacy amplification can be realized by time-division multiplexing with the same set of devices. In addition, we tested the idea from the perspective of error correction and privacy amplification, respectively. The analysis results show that the existing error correction algorithms and their corresponding hash function families or the common privacy amplification methods and their corresponding error-correcting codes cannot realize time-division multiplexing for error correction and privacy amplification temporarily. However, according to the principle of correspondence between error-correcting codes and hash function families, the idea of time-division multiplexing is possible. Moreover, the research on time-division multiplexing for error correction and privacy amplification has some practical significance. Once the idea of time-division multiplexing is realized, it will further reduce the calculation and storage cost of the post-processing process, reduce the deployment cost of quantum key distribution, and help to remote the practical engineering of quantum key distribution. [ABSTRACT FROM AUTHOR]

A binary constant weight code is a type of error-correcting code with a wide range of applications. The problem of finding a binary constant weight code has long been studied as a combinatorial optimization problem in coding theory. In this paper, we propose a quantum search algorithm for binary constant weight codes. Specifically, the search problem is formulated as a polynomial binary optimization problem and Grover adaptive search is used for providing the quadratic speedup. Focusing on the inherent structure of the problem, we derive an upper bound on the minimum of the objective function value and a lower bound on the exact number of solutions. By exploiting these two bounds, we successfully reduced the constant overhead of the algorithm, although the overall query complexity remains exponential due to the NP-complete nature of the problem. In our algebraic analysis, it was found that this proposed algorithm is capable of reducing the number of required qubits, thus enhancing the feasibility. Additionally, our simulations demonstrated that it reduces the average number of classical iterations by 63% as well as the average number of total Grover rotations by 31%. The proposed approach may be useful for other quantum search algorithms and optimization problems. [ABSTRACT FROM AUTHOR]

The correction notice addresses errors in the parameters and theorems of the article "Quantum error-correcting codes from the quantum construction X." Adjustments were made to Theorems 2.9, 3.2, 3.7, 3.9, Lemma 3.14, Theorems 3.15, 3.16, and 3.20 to provide accurate information on quantum error-correcting codes. Tables 2 and 3 compare and present new Quantum Error Correction (QEC) codes from the corrected theorems, offering valuable information for researchers studying quantum error correction codes. The acknowledgements thank Markus Grassl for identifying the mistakes, and the data availability section clarifies that no datasets were generated or analyzed in the study. [Extracted from the article]

Inspired by classical polar codes, whose coding rate can asymptotically achieve the Shannon capacity, researchers are trying to find their analogs in the quantum information field, which are called quantum polar codes. However, no one has designed a quantum polar coding scheme that applies to quantum computing yet. There are two intuitions in previous research. The first is that directly converting classical polar coding circuits to quantum ones will produce the polarization phenomenon of a pure quantum channel, which has been proved in our previous work. The second is that based on this quantum polarization phenomenon, one can design a quantum polar coding scheme that applies to quantum computing. There are several previous work following the second intuition, none of which has been verified by experiments. In this paper, we follow the second intuition and propose a more reasonable quantum polar stabilizer code construction algorithm than any previous ones by using the theory of stabilizer codes. Unfortunately, simulation experiments show that even the stabilizer codes obtained from this more reasonable construction algorithm do not work, which implies that the second intuition leads to a dead end. Based on the analysis of why the second intuition does not work, we provide a possible future direction for designing quantum stabilizer codes with a high coding rate by borrowing the idea of classical polar codes. Following this direction, we find a class of quantum stabilizer codes with a coding rate of 0.5, which can correct two of the Pauli errors. [ABSTRACT FROM AUTHOR]

In this article we will approach the soft-decision decoding for the linear block codes, is a kind of decoding algorithms used to decode data to form better original estimated received message, it is considered as a NP-hard problem. In this article we present a new decoder using memetic algorithm such metaheuristic technic operates on the dual code rather than the code itself that aims to find the error caused when sending a codeword calculated from a message of k bits of information, the resulting codeword contains n bits, including the redundancy bits, the efficiency of an error-correcting code is equivalent to the ratio k/n, the rate is belong the interval [0,1]. Hence a good code is the one that ensures a certain error correcting capability at minimum ratio. The results proved that this approach using a combination of genetic algorithm and local search algorithm provides a sufficiently good solution to an optimization problem; the new decoder is applied on linear codes where the structure is given by a parity check matrix. [ABSTRACT FROM AUTHOR]

Motivated by applications in DNA storage, we study a setting in which strings are affected by tandem-duplication errors. In particular, we look at two settings: disjoint tandem-duplication errors, and equal-length tandem-duplication errors. We construct codes, with positive asymptotic rate, for the two settings, as well as for their combination. Our constructions are duplication-free codes, comprising codewords that do not contain tandem duplications of specific lengths. Additionally, our codes generalize previous constructions, containing them as special cases. [ABSTRACT FROM AUTHOR]

Let p be an odd prime and r, s, m be positive integers. In this study, we initiate our exploration by delving into the intricate structure of all repeated-root cyclic codes and their duals with a length of 2 r p s over the finite field F p m . Through the utilization of CSS and Steane's constructions, a series of new quantum error-correcting (QEC) codes are constructed with parameters distinct from all previous constructions. Furthermore, we identify all maximum distance separable (MDS) cyclic codes of length 2 r p s , which are further utilized in the construction of QEC MDS codes. Finally, we introduce a significant number of novel entanglement-assisted quantum error-correcting (EAQEC) codes derived from these repeated-root cyclic codes. Notably, these newly constructed codes exhibit parameters distinct from those of previously known constructions. [ABSTRACT FROM AUTHOR]

Abstract The post-processing of quantum key distribution mainly includes error correction and privacy amplification. The error correction algorithms and privacy amplification methods used in the existing quantum key distribution are completely unrelated. Based on the principle of correspondence between error-correcting codes and hash function families, we proposed the idea of time-division multiplexing for error correction and privacy amplification for the first time. That is to say, through the common error correction algorithms and their corresponding hash function families or the common hash function families and their corresponding error-correcting codes, error correction and privacy amplification can be realized by time-division multiplexing with the same set of devices. In addition, we tested the idea from the perspective of error correction and privacy amplification, respectively. The analysis results show that the existing error correction algorithms and their corresponding hash function families or the common privacy amplification methods and their corresponding error-correcting codes cannot realize time-division multiplexing for error correction and privacy amplification temporarily. However, according to the principle of correspondence between error-correcting codes and hash function families, the idea of time-division multiplexing is possible. Moreover, the research on time-division multiplexing for error correction and privacy amplification has some practical significance. Once the idea of time-division multiplexing is realized, it will further reduce the calculation and storage cost of the post-processing process, reduce the deployment cost of quantum key distribution, and help to remote the practical engineering of quantum key distribution.

Weighted projective spaces are natural generalizations of projective spaces with a rich structure. Projective Reed–Muller codes are error-correcting codes that played an important role in reliably transmitting information on digital communication channels. In this case study, we explore the power of commutative and homological algebraic techniques to study weighted projective Reed–Muller (WPRM) codes on weighted projective spaces of the form ℙ(1, 1,b). We compute minimal free resolutions and thereby obtain Hilbert series for the vanishing ideal of the 픽q-rational points, and compute main parameters for these codes. [ABSTRACT FROM AUTHOR]

In this article, we find several novel and efficient quantum error-correcting codes ( Q ecc) by studying the structure of constacyclic ( C cc ), cyclic ( C c ), and negacyclic codes (N C c ) over the ring A k = Z p r 1 , r 2 , ⋯ , r k / ⟨ (r b (m b + 1) - r b) , r l r b = r b r l = 0 , b ≠ l ⟩ , where p = q m for m, m b ∈ N , m b | - 1 + q ∀ b , l ∈ 1 to k , q ≥ 3 is a prime, Z p is a finite field. We define distance-preserving gray map δ k . Moreover, we determine the quantum singleton defect (Q SD) of Q ecc, which indicates their overall quality. We compare our codes with existing codes in recent publications. The rings discussed by Kong et al. (EPJ Quantum Technol 10:1–16, 2023), Suprijanto et al. (Quantum codes constructed from cyclic codes over the ring F q + vF q + v 2 F q + v 3 F q + v 4 F q , pp 1–14, 2021. arXiv: 2112.13488v2 [cs.IT]), and Dinh et al. (IEEE Access 8:194082–194091, 2020) are specific cases of our work. Furthermore, we construct several novel and optimum linear complementary dual (Lcd) codes over A k. [ABSTRACT FROM AUTHOR]

The rank of adjacency matrix plays an important role in construction of linear codes from a directed strongly regular graph using different techniques, namely, code orthogonality, adjacency matrix determinant and adjacency matrix spectrum. The problem of computing the dimensions of such codes is an intriguing one. Several conjectures to determine the rank of adjacency matrix of a DSRG Γ over a finite field, keep researchers working in this area. To address the same to an extent, we have considered the problem of finding the rank over a finite field of the adjacency matrix of a DSRG Γ (v , k , t , λ , μ) with μ = 1 , including some mixed Moore graphs and corresponding codes arising from them, in this paper. [ABSTRACT FROM AUTHOR]

High temperatures have dramatic negative effects on interconnect performance. In a bus, whenever the state transitions from "0" to "1", or "0" to "1", joule heating causes the temperature to rise. A low-power error-correcting cooling (LPECC) code, introduced in Chee et al. (IEEE Trans Inf Theory 64:3062–3085, 2018), is a coding scheme which can be used to control the peak temperature, the average power consumption of on-chip buses and error-correction for the transmitted information, simultaneously. In this paper, we show upper bounds and some lower bounds of LPECC codes by some combinatorial configurations, and also present several families of optimal LPECC codes. [ABSTRACT FROM AUTHOR]

In this paper, we use multivariate polynomial rings to construct quantum error-correcting codes (QECCs) via Hermitian construction. We establish a relation between linear codes and ideals of multivariate polynomial rings. We give a necessary and suffcient condition for a multivariate polynomial to generate a Hermitian dual-containing code. By comparing with the literatures in recent years, we construct 31 new QECCs over F q , where q = 3 , 4 , 5 , 7 . Some of them reach quantum singleton bound and some of them exceed quantum GV bound. [ABSTRACT FROM AUTHOR]

Traceability via quick response (QR) codes is regarded as a clever way to learn specifics about a product's history, from its creation to its transit and preservation before reaching consumers. The QR code can, however, be easily copied and faked. Therefore, we suggest a novel strategy to prevent tampering with this code. The method is divided into two primary phases: concealing a security element in the QR code and determining how similar the QR code on the goods is to the real ones. For the first problem, error-correcting coding is used to encode and decode the secret feature in order to manage faults in noisy communication channels. A deep neural network is used to both conceal and extract the information encoded in a QR code, and the suggested network creates watermarked QR code images with good quality and noise tolerance. The network has the ability to be resilient to actual distortions brought on by the printing and photographing processes. In order to measure the similarity of QR codes, we create neural networks based on the Siamese network design. To assess whether a QR code is real or fraudulent, the hidden characteristic extracted from the acquired QR code and the outcome of QR code similarity estimation are merged. With an average accuracy of 98%, the proposed technique performs competitively and has been used in practice for QR code authentication. [ABSTRACT FROM AUTHOR]

Fault-tolerant operations based on stabilizer codes are the state of the art in suppressing error rates in quantum computations. Most such codes do not permit a straightforward implementation of non-Clifford logical operations, which are necessary to define a universal gate set. As a result, implementations of these operations must use either error-correcting codes with more complicated error correction procedures or gate teleportation and magic states, which are prepared at the logical level, increasing overhead to a degree that precludes near-term implementation. Here, we implement a small quantum algorithm, one-qubit addition, fault-tolerantly on a trapped-ion quantum computer, using the [[ 8, 3, 2]] color code. By removing unnecessary error correction circuits and using low-overhead techniques for fault-tolerant preparation and measurement, we reduce the number of error-prone two-qubit gates and measurements to 36. We observe arithmetic errors with a rate of ~1.1 x 10-3 for the fault-tolerant circuit and ~9.5 x 10-3 for the unencoded circuit. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a novel class of real number codes termed as ℝ-spectral codes, derived from real symmetric operators. Our focus is on addressing the challenges associated with error correction in communication systems utilizing real number codes. Our study initiates with a meticulous definition and analysis of the fundamental properties of ℝ-spectral codes. These properties serve as the foundation for comprehending the distinctive characteristics that ℝ-spectral codes offer, ensuring the integrity and reliability of transmitted data. Our exploration extends to the construction of maximum distance separable (MDS) ℝ-spectral codes, which boast the maximum error correction capability. As a culmination of our research, we present an efficient decoding technique tailored for ℝ-spectral codes. Leveraging an MDS ℝ-spectral code and our decoding technique, we achieve optimal error correction and ensure good numerical stability. This innovative approach opens new avenues for enhancing the performance of real-number codes in practical applications. [ABSTRACT FROM AUTHOR]

The error-correcting pair is a general algebraic decoding method for linear codes. Since every linear code is contained in an MDS linear code with the same minimum distance over some finite field extensions, we focus on MDS linear codes. Recently, He and Liao showed that for an MDS linear code 풞 with minimum distance 2ℓ + 2, if it has an ℓ-error-correcting pair, then the parameters of the pair have three possibilities. Moreover, for the first case, they gave a necessary condition for an MDS linear code 풞 with minimum distance 2ℓ + 2 to have an ℓ-error-correcting pair, and for the other two cases, they only gave some counterexamples. For the second case, in this paper, we give a necessary condition for an MDS linear code 풞 with minimum distance 2ℓ + 2 to have an ℓ-error-correcting pair, and then basing on the Product Singleton Bound, we prove that there are two cases for such pairs, and then give some counterexamples basing on twisted generalized Reed–Solomon codes for these cases. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the simple current orbifold of a rational Narain CFT (Narain RCFT). This is a method of constructing other rational CFTs from a given rational CFT, by 'orbifolding' the global symmetry formed by a particular primary fields (called the simple current). Our main result is that a Narain RCFT satisfying certain conditions can be described in the form of a simple current orbifold of another Narain RCFT, and we have shown how the discrete torsion in taking that orbifold is obtained. Additionally, the partition function can be considered a simple current orbifold with discrete torsion, which is determined by the lattice and the B-field. We establish that the partition function can be expressed as a polynomial, with the variables substituted by certain q -series. In a specific scenario, this polynomial corresponds to the weight enumerator polynomial of an error-correcting code. Using this correspondence to the code theory, we can relate the B-field, the discrete torsion, and the B-form to each other. [ABSTRACT FROM AUTHOR]

Quantum comparators hold substantial significance in the scientific community as fundamental components in a wide array of algorithms. In this research, we present an innovative approach where we explore the realm of comparator circuits, specifically focussing on three distinct circuit designs present in the literature. These circuits are notable for their use of T-gates, which have gained significant attention in circuit design due to their ability to enable the utilisation of error-correcting codes. However, it is important to note that T-gates come at a considerable computational cost. One of the key contributions of our work is the optimisation of the quantum gates used within these circuits. We articulate the proposed circuits employing Clifford+T gates, facilitating error correction code implementation. Additionally, we minimise T-gate usage, thereby reducing computational costs and fortifying circuit robustness against errors and environmental disturbances-essential for mitigating the effects of internal and external noise. Our methodology employs a bottom-up examination of comparator circuits, initiating with a detailed study of their gates. Subsequently, we systematically dissect the functions of these gates, thereby advancing towards a comprehensive understanding of the circuit's overall functionality. This meticulous examination forms the foundation of our research, enabling us to identify areas where optimisations can be made to improve their performance. [ABSTRACT FROM AUTHOR]

There are various metrics for researching error-correcting codes. Especially, high-density data storage system gives the existence of inconsistency for the reading and writing process. The symbol-pair metric is motivated for outputs that have overlapping pairs of symbols in a certain channel. The Rosenbloom–Tsfasman (RT) metric is introduced since there exists a problem that is related to transmission over several parallel communication channels with some channels not available for the transmission. In this paper, we determine the minimum symbol-pair weight and RT weight of repeated-root cyclic codes over R = F p m [ u ] / ⟨ u 4 ⟩ of length n = p k . For the determination, we explicitly present third torsional degree for all different types of cyclic codes over R of length n. [ABSTRACT FROM AUTHOR]

Quantum error-correcting codes and entanglement-assisted quantum error-correcting codes have important applications in quantum computing and quantum communication. In this paper, we construct several classes of quantum MDS codes and entanglement-assisted quantum MDS codes by using generalized Reed-Solomon codes. The parameters of most of the codes constructed are new. [ABSTRACT FROM AUTHOR]

Secret-sharing is a vital topic of cryptography and has widely used in information protection. One technique to the development of secret-sharing schemes is primarily based on error-correcting codes. In this paper, we determine the minimal codewords of relative four-weight codes and have the utility in the secret sharing schemes. [ABSTRACT FROM AUTHOR]

Offset quadrature amplitude modulation–based filter bank multicarrier (FBMC-OQAM) method is a promising technology for future wireless communication systems. It offers several advantages over traditional orthogonal frequency-division multiplexing (OFDM) modulation, including higher spectral efficiency, lower out-of-band emission, and improved robustness to time-frequency selective channels. Polar codes, a new class of error-correcting codes, have received much attention recently due to their ability to achieve the Shannon limit with practical decoding complexity. This paper analyzed and investigated the error rate performance of polar-coded FBMC-OQAM systems. Our results show that applying polar codes to FBMC-OQAM systems significantly improves the error rate. In addition, we found that employing random code interleavers can yield additional coding gains of up to 0.75 dB in additive white Gaussian noise (AWGN) and 2 dB in Nakagami-m fading channels. Our findings suggest that polar-coded FBMC-OQAM is a promising combination for future wireless communication systems. We also compared turbo-coded FBMC-OQAM for short code lengths, and our simulations showed that polar codes exhibit comparable error-correcting capabilities. These results will be of interest to researchers and engineers working on the advancement of future wireless communication systems. [ABSTRACT FROM AUTHOR]

This paper focuses on studying the properties of constacyclic codes and quantum error-correcting codes. The code is studied over a specific mathematical structure called the ring S, which is defined as S = Iq[u, v]/⟨u² − α², v² − α², uv − vu⟩, where Iq is a finite field of q elements, α be the nonzero elements of the field Iq, and q is a power of an odd prime p such that q = pm, for m≥ 1. The paper also introduces a Gray map and use it to decompose constacyclic codes over the ring S into a direct sum of constacyclic codes over Iq. We construct new and better quantum error-correcting codes over the ring S (cf.; Table 1 and Table 2). Moreover, we also obtain best known linear codes as well as best dimension linear codes (cf.; Table 4). [ABSTRACT FROM AUTHOR]

Sidon sets have several applications in mathematics and in real-world problems, including the generation of secret keys in cryptography, error-correcting codes, and the physical problem of compression of signals in telecommunications. In particular, in cryptography, the design of cryptographic functions with optimal properties like nonlinearity and differential uniformity plays a fundamental role in the development of secure cryptographic systems. Based on the construction of Bose-type Sidon sets, in this paper we present the construction of a new cryptographic function with good properties of nonlinearity and differential uniformity. [ABSTRACT FROM AUTHOR]

BCH codes are an interesting class of cyclic codes with good error-correcting capability and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Let F q be the finite field of size q and n = q m - 1 , where m is a positive integer. Let C (q , m , δ) be the primitive narrow-sense BCH codes of length n over F q with designed distance δ . Denote s = m - t , r = m mod s and λ = ⌊ t / s ⌋ . In this paper, we mainly investigate the dimensions and Bose distances of the codes C (q , m , δ) with designed distance of the following two types: δ = q t + h , ⌈ m 2 ⌉ ≤ t < m , 0 ≤ h < q s + ∑ i = 1 λ - 1 q r + i s ; δ = q t - h , ⌈ m 2 ⌉ < t < m , 0 ≤ h < (q - 1) ∑ i = 1 s q i . This extensively extends the results on Bose distance in Ding et al (IEEE Trans Inf Theory 61(5):2351–2356, 2015). Moreover, the parameters of the hulls of the BCH code C (q , m , q t) are studied in some cases. [ABSTRACT FROM AUTHOR]

The Reed–Muller codes are a family of error-correcting codes that have been widely studied in coding theory. In 2020, Yan and Lin introduced a variant of Reed–Muller codes called symmetric Reed–Muller codes. We investigate linear maps of the automorphism group of symmetric Reed–Muller codes and show that the set of these linear maps forms a subgroup of the general linear group, which is the automorphism group of punctured Reed–Muller codes.We provide a method to determine all the automorphisms in this subgroup explicitly for some special cases. [ABSTRACT FROM AUTHOR]

The homogeneous weight (metric) is useful in the construction of codes over a ring of integers Z p l (p prime and l ≥ 1 an integer). It becomes Hamming weight when the ring is taken to be a finite field and becomes Lee weight when the ring is taken to be Z 4 . This paper presents homogeneous weight distribution and total homogeneous weight of burst and repeated burst errors in the code space of n-tuples over Z p l . Necessary and sufficient conditions for existence of an (n, k) linear code over Z p l correcting the error patterns with respect to the homogeneous weight are derived. [ABSTRACT FROM AUTHOR]

Given the growing urge for plastic management and regulation in the world, recent studies have investigated the problem of plastic material identification for correct classification and disposal. Recent works have shown the potential of machine learning techniques for successful microplastics classification using Raman signals. Classification techniques from the machine learning area allow the identification of the type of microplastic from optical signals based on Raman spectroscopy. In this paper, we investigate the impact of high-frequency noise on the performance of related classification tasks. It is well-known that classification based on Raman is highly dependent on peak visibility, but it is also known that signal smoothing is a common step in the pre-processing of the measured signals. This raises a potential trade-off between high-frequency noise and peak preservation that depends on user-defined parameters. The results obtained in this work suggest that a linear discriminant analysis model cannot generalize properly in the presence of noisy signals, whereas an error-correcting output codes model is better suited to account for inherent noise. Moreover, principal components analysis (PCA) can become a must-do step for robust classification models, given its simplicity and natural smoothing capabilities. Our study on the high-frequency noise, the possible trade-off between pre-processing the high-frequency noise and the peak visibility, and the use of PCA as a noise reduction technique in addition to its dimensionality reduction functionality are the fundamental aspects of this work. [ABSTRACT FROM AUTHOR]

CSS-T codes were recently introduced as quantum error-correcting codes that respect a transversal gate. A CSS-T code depends on a CSS-T pair, which is a pair of binary codes (C 1 , C 2) such that C 1 contains C 2 , C 2 is even, and the shortening of the dual of C 1 with respect to the support of each codeword of C 2 is self-dual. In this paper, we give new conditions to guarantee that a pair of binary codes (C 1 , C 2) is a CSS-T pair. We define the poset of CSS-T pairs and determine the minimal and maximal elements of the poset. We provide a propagation rule for nondegenerate CSS-T codes. We apply some main results to Reed–Muller, cyclic and extended cyclic codes. We characterize CSS-T pairs of cyclic codes in terms of the defining cyclotomic cosets. We find cyclic and extended cyclic codes to obtain quantum codes with better parameters than those in the literature. [ABSTRACT FROM AUTHOR]

Perfect error-correcting codes allow for an optimal transmission of information while guaranteeing error correction. For this reason, proving their existence has been a classical problem in both pure mathematics and information theory. Indeed, the classification of the parameters of e-error correcting perfect codes over q-ary alphabets was a very active topic of research in the late 20th century. Consequently, all parameters of perfect e-error-correcting codes were found if e ≥ 3 , and it was conjectured that no perfect 2-error-correcting codes exist over any q-ary alphabet, where q > 3 . In the 1970s, this was proved for q a prime power, for q = 2 r 3 s and for only seven other values of q. Almost 50 years later, it is surprising to note that there have been no new results in this regard and the classification of 2-error-correcting codes over non-prime power alphabets remains an open problem. In this paper, we use techniques from the resolution of the generalised Ramanujan–Nagell equation and from modern computational number theory to show that perfect 2-error-correcting codes do not exist for 172 new values of q which are not prime powers, substantially increasing the values of q which are now classified. In addition, we prove that, for any fixed value of q, there can be at most finitely many perfect 2-error-correcting codes over an alphabet of size q. [ABSTRACT FROM AUTHOR]

Polar codes are the popular error-correcting codes and increased their attention after being adopted for the control channel in fifth-generation new radio (5G NR) standards. An efficient hardware architecture for polar code is often required with minimal encoding and decoding complexity. This work proposes a Multi-folded pipelined architecture and analyzes the performance in terms of latency, hardware utilization, and throughput. The designed architecture has two folded architectures interconnected in parallel to output 4-bits simultaneously. Folding transformations are used to reduce the number of idle processing elements (PEs) in every stage leading to the effective utilization of PE. Precomputation is effectively utilized in the PE to reduce the critical path delay, which improves the maximum operating frequency. A Loop-based shifting register (LSR) is employed to reduce the number of registers used. The analytical model for latency and utilization rate has been derived from the scheduling of the proposed architecture. The proposed design shows 63–71% higher hardware utilization than conventional semi-parallel design for code length N = 512 suitable for the physical downlink control channel (PDCCH) in 5G NR. The architecture is also implemented in Virtex-6, ZYNQ-Ultrascale+ MPSoC device for maximum supported code length of 5G NR, i.e., up to 2 10 , compared with the existing decoders. The proposed design also has the benefit of lesser look-up-table (LUT) consumption and zero random-access-memory (RAM) usage with some additional registers, making it suitable for resource-constraint applications. [ABSTRACT FROM AUTHOR]

Quantum error correction codes based on continuous variables play an important role for the implementation of quantum communication systems. A natural application of such codes occurs within quantum repeater systems which are used to combat severe channel losses and local gate errors. In particular, channel loss drastically reduces the distance of communication between remote users. Here, a cavity‐quantum electrodynamics (QED) based repeater scheme is considered to address the losses in the quantum channel. This repeater scheme relies on the transmission of a specific class of rotationally invariant error‐correcting codes. Several rotation‐symmetric bosonic codes (RSBCs) are compared for encoding the initial states of two remote users connected by a quantum repeater network against the convention of the cat codes and the performance of the system is quantified by using the secret key rate. In particular, the number of stations required to exchange a secret key over a fixed distance is determined and establish the resource overhead. For higher‐loss codes, the results show that a secret key rate (SKR) value of 0.01 bit per channel use can be achieved at a distance of 10000 km, with an elementary distance of 1.3 km. [ABSTRACT FROM AUTHOR]

Low-density parity check (LDPC) codes, are a family of error-correcting codes, their performances close to the Shannon limit make them very attractive solutions for digital communication systems. There are several algorithms for decoding LDPC codes that show great diversity in terms of performance related to error correction. Also, very recently, many research papers involved the genetic algorithm (GA) in coding theory, in particular, in the decoding linear block codes case, which has heavily contributed to reducing the bit error rate (BER). In this paper, an efficient method based on the GA is proposed and it is used to improve the power of correction in terms of BER and the frame error rate (FER) of LDPC codes. Subsequently, the proposed algorithm can independently decide the most suitable moment to stop the decoding process, moreover, it does not require channel information (CSI) making it adaptable for all types of channels with different noise or intensity. The simulations show that the proposed algorithm is more efficient in terms of BER compared to other LDPC code decoders. [ABSTRACT FROM AUTHOR]

In this work, the performance of coded continuous phase modulation (CPM) transceivers for orthogonal frequency-division multiplexing (OFDM) in underwater acoustic channels is evaluated. The proposed technique employs the Bose–Chaudhuri–Hocquenghem (BCH) class of cyclic codes, and a CPM-based mapper is being used in place of a traditional OFDM mapper. Bit-error-rates (BERs) for various distances are evaluated. We use the Bellhop acoustic channel simulator that is considered to be very close to a real underwater channel. The performance of the proposed system is evaluated for 23 values of the CPM modulation index h as a function of the distance between the transmitter (Tx) and receiver (Rx). Based upon the error performance, we identified several best-performing CPM indices. We also observed that for Tx–Rx distances of 100 and 250 m, the proposed system gives acceptable performance without the need for equalization. We also compared the out-of-band radiation of the proposed system with PSK-OFDM and observed that the uncoded CPM-OFDM has a better out-of-band (OOB) performance than the traditional OFDM. Moreover, a comparison of BERs with the traditional PSK-OFDM system shows that the proposed system outperforms the traditional OFDM system by a wide margin. [ABSTRACT FROM AUTHOR]

In this paper, a channel-optimized quantum communication scheme with imperfect Bell states is being considered, based on quantum teleportation and error correction codes technology. In this scheme, a novel "combination code" technique is proposed to protect the pre-shared Bell states from storage errors and to safeguard the information-encoded states from noisy channels. Ultimately, it is revealed by Monte Carlo simulation results that the channel fidelity of the proposed channel-optimized quantum communication scheme with imperfect Bell states is significantly advantageous over standard quantum error-correcting code (QECC) and entanglement-assisted quantum error-correcting code (EAQECC) communication schemes. [ABSTRACT FROM AUTHOR]

While several papers have explored the application of deep learning for COVID-19 detection in chest X-ray images, the consideration of images taken under emergency conditions remains limited. In this paper, we define emergency conditions as situations where inevitable errors occur during X-ray imaging in severe respiratory conditions of COVID-19 patients. These errors include positioning errors, protocol parameter errors, and motion artifacts. Our research aims to propose an intelligent tool based on deep neural networks and ensemble learning to detect COVID-19 cases from chest X-ray images in both standard and emergency conditions. As comprehensive datasets incorporating emergency images are scarce, we first generated a local dataset by investigating COVID-19 cases in our local hospital. We specifically selected cases with the aforementioned errors caused by emergency conditions. This dataset comprises patients in acute situations, as well as technical radiographic errors resulting from a significant number of people requiring radiography images. We evaluated the performance of recent popular pre-trained deep neural networks on our local dataset, which highlighted the importance of considering such emergency images. Subsequently, we transfer-learned 11 popular deep neural networks using our local dataset. Furthermore, we identified the transferred neural networks with the highest accuracies (exceeding 95% accuracy) and implemented ensemble learning methods such as Majority Voting and Error-Correcting Output Codes (ECOC). Our proposed methods excel in identifying COVID-19 in both emergency and non-emergency chest X-rays with high accuracy. [ABSTRACT FROM AUTHOR]

In order to improve the multi-class assessment performance of transient stability in power systems, a multi-class assessment model that combines the CLV-GAN algorithm with an improved error-correcting output coding technique is proposed in the paper. To address the issue of the small number of unstable samples in power systems, a sample generation model is constructed by combining a dual-encoder VAE with a GAN network. The model generates effective artificial samples to balance the sample ratio between categories by learning the latent distribution of aperiodic and oscillatory unstable samples from the distribution. The decomposition method based on an improved error-correcting output coding algorithm is applied to convert the multi-class problem into a decision fusion issue for binary models. This method improves the overall performance of the multi-class model, particularly significantly increasing the recognition accuracy of discrimination against oscillatory unstable samples and reducing the safety hazards in the operation of power systems. The simulation validation was conducted on the IEEE 39-bus and IEEE 140-bus systems to confirm the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

In communication technologies such as digital watermarking, wireless sensor networks (WSNs), and visual light communication (VLC), error-correcting codes are crucial. The Enhanced Hadamard Error-Correcting Code (EHC), which is based on 2D Hadamard Basis Images, is a novel error correction technique that is presented in this study. This technique is used to evaluate the effectiveness of the video watermarking scheme. Even with highly sophisticated embedding techniques, watermarks usually fail to resist such comprehensive attacks because of the extraordinarily high compression rate of approximately 1:200 that is frequently employed in video dissemination. It can only be used in conjunction with a sufficient error-correcting coding method. This study compares the efficacy of the well-known Reed–Solomon Code with this novel technique, the Enhanced Hadamard Error-Correcting Code (EHC), in maintaining watermarks in embedded videos. The main idea behind this newly created multidimensional Enhanced Hadamard Error-Correcting Code is to use a 1D Hadamard decoding approach on the 2D base pictures after they have been transformed into a collection of one-dimensional rows. Following that, the image is rebuilt, allowing for a more effective 2D decoding procedure. Using this technique, it is possible to exceed the theoretical error-correcting capacity threshold of ⌊ d m i n − 1 2 ⌋ bits, where d m i n is the Hamming distance. It may be possible to achieve better results by converting the 2D EHC into a 3D format. The new Enhanced Hadamard Code is used in a video watermarking coding scheme to show its viability and efficacy. The original video is broken down using a multi-level interframe wavelet transform during the video watermarking embedding process. Low-pass filtering is applied to the video stream in order to extract a certain frequency range. The watermark is subsequently incorporated using this filtered section. Either the Reed–Solomon Correcting Code or the Enhanced Hadamard Code is used to protect the watermarks. The experimental results show that EHC far outperforms the RS Code and is very resilient against severe MPEG compression. [ABSTRACT FROM AUTHOR]

Let p be an odd prime with p ≠ 5 . In this paper, we first provide the structures of repeated-root cyclic codes of length 10 p s over finite fields F p m . We then give two methods of constructing good quantum error-correcting (QEC) codes from repeated-root cyclic codes of length 10 p s over finite fields F p m . By means of the dimensions of repeated-root cyclic codes of length 10 p s over finite fields F p m , we exhibit an effective manner for constructing new EAQEC codes. We show that the usage of these methods brings us many good QEC and EQAEC codes having these advantages: (1) the parameters of our QEC and EQAEC codes are different from all the previous constructions; (2) for repeated-root cyclic codes, our methods allows for easily calculating the dimensions of QEC and EQAEC codes, and the numbers c of pre-shared maximally entangled states of EAQEC codes. [ABSTRACT FROM AUTHOR]

Numerous soft faults in SRAM memory emerge as technological innovations scales down, resulting in single and several cell upsets. The increased use of transistors in space applications has rendered semiconductor devices more vulnerable to soft errors caused by harm from radiation. A single event upset (SEU) is occurring whenever a soft error produces a tiny bit flipped in a storage device. Because SEU faults affect system performance, they must be addressed as soon as possible. Error-correcting codes, like the method known as (7,4) hamming codes, were devised and their decoding and encoding procedures were verified. It also used to detect single errors that can be fixed. It also helps detect double errors, SECDED however repair of double errors is tough. The decoding and encoding techniques of these approaches were investigated, and all computational findings had been verified and executed in a Xilinx NEXYS 4 DDR FPGA board. [ABSTRACT FROM AUTHOR]

Entanglement-assisted quantum error-correcting (EAQEC) codes are a generalization of quantum error-correcting (QEC) codes, which can be constructed from arbitrary classical linear codes by relaxing the dual-containing condition and by using preshared entangled states between the sender and the receiver. In this paper, we investigate EAQEC codes of length n = 2 (q 2 + 1) a , where q is an odd prime power, a = m 2 + 1 and m is an odd integer. The resulting EAQEC codes are entanglement-assisted quantum maximum-distance-separable (EAQMDS) codes when the minimum distance d ≤ n + 2 2 . [ABSTRACT FROM AUTHOR]

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A parallel corpus comprising Croatian EU legislative documents automatically translated into English spans 28 years and is enriched with metadata, including creation year and hierarchical classifier tags denoting descriptors, document types, and fields. However, nearly two-thirds of the approximately 1.5 thousand texts lack complete metadata, necessitating labor- intensive manual efforts that pose challenges for human administration. This incompleteness issue can be observed in the case of official legal sites functioning as regular service provisioning databases. In response, this paper introduces an artificial cognitive and multilabel classification approach to expedite the tagging process with only a fraction of the manual effort. Leveraging the Latent Dirichlet Allocation (LDA) algorithm, our method assigns field values or tags to incompletely labeled documents. We implement a Flexible LDA variant, incorporating the influence of topics close to the most probable topic, regulated by a relative probability threshold (RPT). We evaluate the LDA prediction's dependence on document prefiltering and RPT values. Furthermore, we investigate the dependence of quantitative linguistic properties on the type and speciality of pre-processing tasks. Our algorithm, built on error-correcting optimizing codes, successfully predicts a mixture of topic probabilities for these legal texts. This prediction is achieved by calculating the Hamming distance of binary feature vectors created using the legal fields of the EUROVOC multilingual thesaurus. [ABSTRACT FROM AUTHOR]

By generalizing the stabilizer quantum error-correcting codes, entanglement-assisted quantum error-correcting (EAQEC) codes were introduced, which could be derived from any classical linear codes via the relaxation of self-orthogonality conditions with the aid of pre-shared entanglement between the sender and the receiver. In this paper, three classes of entanglement-assisted quantum error-correcting maximum-distance-separable (EAQMDS) codes are constructed through generalized Reed–Solomon codes. Under our constructions, the minimum distances of our EAQMDS codes are much larger than those of the known EAQMDS codes of the same lengths that consume the same number of bits. Furthermore, some of the lengths of the EAQMDS codes are not divisors of q 2 - 1 , which are completely new and unlike all those known lengths existed before. [ABSTRACT FROM AUTHOR]

Maximum distance separable (MDS) quantum error-correcting codes (QECCs) and MDS entanglement-assisted QECCs (EAQECCs) play significant roles in quantum information theory. In this paper, we construct several new families of MDS QECCs and MDS EAQECCs by utilizing Hermitian self-orthogonal generalized Reed–Solomon codes. These newly obtained MDS QECCs contain some known classes of MDS QECCs as subclasses and some of them have larger minimum distance. In addition, many q-ary MDS QECCs and MDS EAQECCs in our constructions have length exceeding q + 1 and minimum distance surpassing q 2 + 1 . [ABSTRACT FROM AUTHOR]