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As a particular subclass of cyclic codes, BCH codes have wide applications in storage devices, communication systems, consumer electronics and other fields. However, parameters of BCH codes are unknown in general. In this paper, we investigate parameters of BCH codes of length q m + 1 λ where λ ∣ q + 1 .Some new techniques are employed to study the coset leaders. For any odd prime power q and m = 4 , 8 , or m ≥ 12 and m ≡ 4 (mod 8) , the second, the third and the fourth largest coset leaders modulo q m + 1 are determined, and the dimensions of some BCH codes of length q m + 1 with large designed distances are given. For 1 < λ < q + 1 , the first few largest coset leaders and the coset leaders modulo q m + 1 λ in the range 1 to q ⌊ (m + 1) / 2 ⌋ λ are studied, and the dimensions of some BCH codes of length q m + 1 λ are given as well. The BCH codes presented in this paper are LCD codes and have a sharper lower bound on the minimum distance than the well-known BCH bound. [ABSTRACT FROM AUTHOR]

Telecommand (TC) plays a crucial role in the success of high-altitude balloon experiments. Bose, Ray-Chaudhuri, Hocquenghem (BCH) codes are commonly employed to ensure reliable command operation. The Balloon Facility (BF) of Tata Institute of Fundamental Research (TIFR) uses a TC system based on BCH (31,16) coding technique, to control balloon and payload operations. This paper presents prototyping and implementation of TC encoder and decoder using Spartan 6 Field Programmable Gate Array (FPGA). The code is written in Very high-speed integrated circuit Hardware Description Language (VHDL). Simulation and synthesis are done using Xilinx ISE 14.7 design suite. Simulation results show the design is robust. The TC encoder is implemented in a commercial FPGA development board and the TC decoder is implemented in a specially designed FPGA board, successfully. This paper presents the salient features of the TC system in use and the implementation of the system using FPGA. [ABSTRACT FROM AUTHOR]

Negacyclic BCH codes are a generalization of BCH codes, they have better parameters than BCH codes in some cases. In this paper, we investigate negacyclic BCH codes of length q m + 1 2 and q m - 1 2 λ over F q , where q ≥ 3 is an odd prime power and λ is an integer with 2 ≤ λ ≤ q - 1 , λ ∣ (q - 1) and 2 λ ∣ (q m - 1) . By using some results on the q-cyclotomic cosets modulo q m + 1 or q m - 1 λ , we determine the dimensions of these two classes of negacyclic BCH codes, and give some lower bounds on the minimum distance of these codes. [ABSTRACT FROM AUTHOR]

The Bose-Chaudhuri-Hocquenghem (BCH) codes are a well-studied subclass of cyclic codes that have found numerous applications in error correction and notably in quantum information processing. They are widely used in data storage and communication systems. A subclass of attractive BCH codes is the narrow-sense BCH codes over the Galois field ${\mathrm {GF}}(q)$ with length $q+1$ , which are closely related to the action of the projective general linear group of degree two on the projective line. Despite its interest, not much is known about this class of BCH codes. This paper aims to study some of the codes within this class and specifically narrow-sense antiprimitive BCH codes (these codes are also linear complementary duals (LCD) codes that have interesting practical recent applications in cryptography, among other benefits). We shall use tools and combine arguments from algebraic coding theory, combinatorial designs, and group theory (group actions, representation theory of finite groups, etc.) to investigate narrow-sense antiprimitive BCH Codes and extend results from the recent literature. Notably, the dimension, the minimum distance of some $q$ -ary BCH codes with length $q+1$ , and their duals are determined in this paper. The dual codes of the narrow-sense antiprimitive BCH codes derived in this paper include almost MDS codes. Furthermore, the classification of ${\mathrm {PGL}}(2, p^{m})$ -invariant codes over ${\mathrm {GF}}(p^{h})$ is completed. As an application of this result, the $p$ -ranks of all incidence structures invariant under the projective general linear group ${\mathrm {PGL}}(2, p^{m})$ are determined. Furthermore, infinite families of narrow-sense BCH codes admitting a 3-transitive automorphism group are obtained. Via these BCH codes, a coding-theory approach to constructing the Witt spherical geometry designs is presented. The BCH codes proposed in this paper are good candidates for permutation decoding, as they have a relatively large group of automorphisms. [ABSTRACT FROM AUTHOR]

Linear codes with complementary duals (LCD codes) have attracted a lot of interest in recent years because of their applications in implementations against side-channel attacks and fault injection attacks. In this paper, we investigate the parameters of ternary LCD constacyclic BCH codes of lengths 3 m - 1 / 2 and 3 m + 1 / 2. For length n = 3 m - 1 / 2 , the parameters of LCD negacyclic BCH codes are explored by calculating the first several largest odd absolute coset leaders modulo 3 m - 1 , and the minimum distance of a class of such LCD codes are settled. For length n = 3 m + 1 / 2 , the parameters of ternary LCD cyclic BCH codes with designed distance 2 ≤ δ ≤ 3 m / 2 + 2 are discussed by tracing coset leaders modulo 3 m + 1 / 2. Some of these BCH codes that are LCD with exact minimum distance are presented. [ABSTRACT FROM AUTHOR]

Tang and Ding [IEEE IT 67 (2021) 244-254] studied the class of BCH codes $\mathcal {C}_{(q,q+1,4,1)}$ and their dual codes with $q=2^{m}$ and established that the codewords of the minimum (or the second minimum) weight in these codes support 4-designs or 3-designs. Motivated by this, we further investigate the codewords of the next adjacent weight in such codes and discover more infinite classes of $t$ -designs with $t=3,4$. In particular, we prove that codewords of weight 7 in $\mathcal {C}_{(q,q+1,4,1)}$ support 4-designs for odd $m \geqslant 5$ and they support 3-designs for even $m \geqslant 4$ , which provide infinite classes of simple $t$ -designs with new parameters. Another significant class of $t$ -designs we produce in this paper has complementary designs with parameters 4- $(2^{2s+1}+ 1,5,5)$ ; these designs have the smallest index among all the known simple 4- $(q+1,5,\lambda)$ designs derived from codes for prime powers $q$ ; and they are further proved to be isomorphic to the 4-designs admitting the projective general linear group PGL $(2,2^{2s+1})$ as the automorphism group constructed by Alltop in 1969. [ABSTRACT FROM AUTHOR]

It is well-known that cyclic codes have efficient encoding and decoding algorithms. In recent years, antiprimitive BCH codes have attracted a lot of attention. The objective of this paper is to study BCH codes of this type over finite fields and analyse their parameters. Some lower bounds on the minimum distance of antiprimitive BCH codes are given. The BCH codes presented in this paper have good parameters in general, containing many optimal linear codes. In particular, two open problems about the minimum distance of BCH codes of this type are partially solved in this paper. [ABSTRACT FROM AUTHOR]

In this paper, a family of $[{q}^{2}-1, 4, {q}^{2}-{q}-2]$ cyclic codes over ${\mathbb F}_{{q}}$ meeting the Griesmer bound is presented. Their duals are $[{q}^{2}-1,{q}^{2}-5,4]$ almost MDS codes and are optimal with respect to the sphere-packing bound. The ${q}_{0}$ -ary subfield codes of this family of cyclic codes are also investigated, where ${q}_{0}$ is any prime power such that q is power of ${q}_{0}$. Some of the subfield codes are optimal and some have the best known parameters. It is shown that the subfield codes are equivalent to a family of primitive BCH codes and thus the parameters of the BCH codes are solved. The duals of the subfield codes are also optimal with respect to the sphere-packing bound. A family of $[{q}^{2}, 4, {q}^{2}-{q}-1]$ linear codes over ${\mathbb F}_{{q}}$ meeting the Griesmer bound is presented. Their duals are $[{q}^{2},{q}^{2}-4,4]$ almost MDS codes and are optimal with respect to the sphere-packing bound. The ${q}_{0}$ -ary subfield codes of this family of linear codes are also investigated, where ${q}_{0}$ is any prime power such that q is power of ${q}_{0}$. Five infinite families of 2-designs are also constructed with three families of linear codes of this paper. [ABSTRACT FROM AUTHOR]

Two families of asymmetric quantum codes of length n = q 2 m - 1 over F q 2 are constructed in this paper. By a detailed analysis of properties about q 2 -ary cyclotomic cosets modulo n, Hermitian dual-containing conditions for a family of primitive narrow-sense BCH codes are presented. Consequently, a series of asymmetric quantum BCH codes are constructed via the CSS-like construction and pairs of nested BCH codes. The parameters of new asymmetric quantum codes presented here are better than those available in the literatures before, and the real Z-distance are much larger than δ max + 1 . [ABSTRACT FROM AUTHOR]

Self-orthogonal codes are an important type of linear codes due to their wide applications in communication and cryptography. The Euclidean (or Hermitian) hull of a linear code is defined to be the intersection of the code and its Euclidean (or Hermitian) dual. It is clear that the hull is self-orthogonal. The main goal of this paper is to obtain self-orthogonal codes by investigating the hulls. Let $\mathcal {C}_{(r,r^{m}-1,\delta,b)}$ be the primitive BCH code over $\mathbb {F}_{r}$ of length $r^{m}-1$ with designed distance $\delta $ , where $\mathbb {F}_{r}$ is the finite field of order $r$. In this paper, we will present Euclidean (or Hermitian) self-orthogonal codes and determine their parameters by investigating the Euclidean (or Hermitian) hulls of some primitive BCH codes. Several sufficient and necessary conditions for primitive BCH codes with large Hermitian hulls are developed by presenting lower and upper bounds on their designed distances. Furthermore, some Hermitian self-orthogonal codes are proposed via the hulls of BCH codes and their parameters are also investigated. In addition, we determine the dimensions of the code $\mathcal {C}_{(r,r^{2}-1,\delta,1)}$ and its hull in both Hermitian and Euclidean cases for $2 \le \delta \le r^{2}-1$. We also present two sufficient and necessary conditions on designed distances such that the hull has the largest dimension. [ABSTRACT FROM AUTHOR]

The binary quadratic-residue codes and the punctured Reed-Muller codes ${\mathcal {R}}_{2}((m-1)/2, m))$ are two families of binary cyclic codes with parameters $[n, (n+1)/2, d \geq \sqrt {n}]$. These two families of binary cyclic codes are interesting partly due to the fact that their minimum distances have a square-root bound. The objective of this paper is to construct two families of binary cyclic codes of length $2^{m}-1$ and dimension near $2^{m-1}$ with good minimum distances. When $m \geq 3$ is odd, the codes become a family of duadic codes with parameters $[2^{m}-1, 2^{m-1}, d]$ , where $d \geq 2^{(m-1)/2}+1$ if $m \equiv 3 \pmod {4}$ and $d \geq 2^{(m-1)/2}+3$ if $m \equiv 1 \pmod {4}$. The two families of binary cyclic codes contain some optimal binary cyclic codes. [ABSTRACT FROM AUTHOR]

The (Euclidean) hull of a linear code is defined to be the intersection of the code and its Euclidean dual. It is clear that the hulls are self-orthogonal codes, which are an important type of linear codes due to their wide applications in communication and cryptography. Let $ \mathcal C_{(2,n,\delta)} $ be the binary primitive narrow-sense BCH code, where $ n = 2^m-1 $ and $ m $ is a positive integer. In this paper, we will investigate the parameters of the hulls of $ \mathcal C_{(2,n,\delta)} $. The dimension of $ \text{Hull}(\mathcal C_{(2,n,\delta)}) $ will be presented when $ 2 \le \delta \le 2^{\lfloor \frac{m}{2} \rfloor+1}+2^{\lceil \frac{m}{2} \rceil-1}-1 $ with $ m \ge 5 $. Furthermore, we give an improvement on lower bounds of the minimum distances of $ \text{Hull}(\mathcal C_{(2,n,\delta)}) $. We also construct a self-orthogonal subcode of $ \text{Hull}(\mathcal C_{(2,n,\delta)}) $ and investigate the parameters of the self-orthogonal code. [ABSTRACT FROM AUTHOR]

Maximum distance separable (MDS) codes are very important in both theory and practice. There is a classical construction of a family of $[{2^{m}+1, 2u-1, 2^{m}-2u+3}]$ MDS codes for $1 \leq u \leq 2^{m-1}$ , which are cyclic, reversible and BCH codes over ${\mathrm {GF}}(2^{m})$. The objective of this paper is to study the quaternary subfield subcodes and quaternary subfield codes of a subfamily of the MDS codes for even $m$. A family of quaternary cyclic codes is obtained. These quaternary codes are distance-optimal in some cases and very good in general. Furthermore, two infinite families of 3-designs from these quaternary codes and their duals are presented. [ABSTRACT FROM AUTHOR]

The IEEE 802.15.6 was established in Feb 2012 due to emergency of wireless body area networks (WBANs). In order to improve the performance of WBANs, the physical (PHY) layer, medium access control (MAC) layer and network layer have been discussed in a number of literatures. Although there are also many previous works on performance analysis for WBANs, a noise free was frequently assumed when contention error is taken into account in MAC layer. It means that in these works bit error rates (BERs) were not taken into consideration adequately. In this paper, we propose the Markov chain Monte Carlo (MCMC) method to analyze performance in the PHY and MAC layers for WBANs, in which BERs are taken into consideration. The BERs are theoretically analyzed depending on different Bose-Chaudhuri-Hocquenghem (BCH) code rates, and then the BCH code rate for every sensor node is optimized in sense of the highest throughput while assuming the signal to noise ratio (SNR) of every sensor node is different. Furthermore, the dependence of throughput on the BER is clearly explained by calculating the access probability for every sensor node in large SNR region. The BCH code was adopted as an example and then adaptive BCH code rates for WBANs were proposed. The application of proposal method to other error correcting codes is straightforward. [ABSTRACT FROM AUTHOR]

Combinatorial t t -designs have been an interesting topic in combinatorics for decades. It is a basic fact that the codewords of a fixed weight in a code may hold a t t -design. Till now only a small amount of work on constructing t t -designs from codes has been done. In this paper, we determine the weight distributions of two classes of cyclic codes: one related to the triple-error correcting binary BCH codes, and the other related to the cyclic codes with parameters satisfying the generalized Kasami case, respectively. We then obtain infinite families of 2 2 -designs from these codes by proving that they are both affine-invariant codes, and explicitly determine their parameters. In particular, the codes derived from the dual of binary BCH codes hold five 3 3 -designs when m = 4 m = 4. [ABSTRACT FROM AUTHOR]

As a special subclass of cyclic codes, BCH codes have wide applications in communication and storage systems. A BCH code of length $n$ over $\mathbb {F}_{q}$ is always relative to an $n$ -th primitive root of unity $\beta $ in an extension field of $\mathbb {F}_{q}$ , and is called a dually-BCH code if its dual is also a BCH code relative to the same $\beta $. The question as to whether a BCH code is a dually-BCH code is in general very hard to answer. In this paper, an answer to this question for primitive narrow-sense BCH codes and projective narrow-sense ternary BCH codes is given. Sufficient and necessary conditions in terms of the designed distances $\delta $ will be presented to ensure that these BCH codes are dually-BCH codes. In addition, the parameters of the primitive narrow-sense BCH codes and their dual codes are investigated. Some lower bounds on minimum distances of the dual codes of primitive and projective narrow-sense BCH codes are developed. Especially for binary primitive narrow-sense BCH codes, the new bounds on the minimum distances of the dual codes improve the classical Sidel’nikov bound, and are also better than the Carlitz and Uchiyama bound for large designed distances $\delta $. The question as to what subclasses of cyclic codes are BCH codes is also answered to some extent. As a byproduct, the parameters of some subclasses of cyclic codes are also investigated. [ABSTRACT FROM AUTHOR]

This investigate paper proposes those latest progresses in the semiconductor industry have headed in the advancement for additional unpredictable segments and systems' architectures Eventually high number of transistors permitting creation procedures with put An higher number from claiming transistors for every zone of the silicon pass on. Accordingly the manufacturing transform would be less and less reliable. Thusly we need will manufacture frameworks that will recognize the presence from securing faults and fuse strategies will endure these faults same time even now delivering a adequate level for administration. In this paper we available the plan and Investigation from claiming issue tolerant 32-bit math Furthermore legitimate unit circlet outlined utilizing those traditional TMR (Triple modular Redundancy) procedure. Also we configuration ALU to attain achieved energy utilization and profoundly dependable utilizing clock Gating. [ABSTRACT FROM AUTHOR]

This paper presents an improved robust data hiding algorithm based on BCH syndrome code (BCH code) technique and without distortion drift technique. The BCH code technique, which can correct the error bits caused by network transmission, packet loss, video-processing operations, various attacks, etc., encodes the embedded data by using BCH code before data hiding. The without distortion drift technique in this paper is that we exploit several paired-coefficients of a 4 × 4 discrete cosine transform (DCT) block to accumulate the embedding induced distortion, and the directions of intra-frame prediction are utilized to avert the distortion drift. It is proved analytically and shown experimentally that the new data hiding algorithm can get more robustness, effectively avert intra-frame distortion drift and get high visual quality. [ABSTRACT FROM AUTHOR]

BCH codes are among the best practical cyclic codes widely used in consumer electronics, communication systems, and storage devices. However, not much is known about BCH codes with large minimum distance. In this paper, we consider narrow-sense BCH codes of length n = qm 1 N with designed distance delta = s q 1n proportional to n, where N divides qm 1 q 1 and 1 leq s leq q 1. We determine both their dimensions and minimum distances. In particular, when N = 1, the codes are primitive, with minimum distance d = s q 1 (qm 1) and dimension k = (q s)m. The general result on code dimensions is achieved by applying generating functions and inverse discrete Fourier transforms to an enumeration problem. [ABSTRACT FROM AUTHOR]

In this paper we study the impact of error control code (ECC) on characteristic distance in wireless sensor network (WSN). In WSN nodes are energy constrained and the goal is to design an energy efficient network. Characteristic distance is important for such network. We consider Bose, Chaudhuri and Hocquenghem and Reed-Solomon codes with different error correction capabilities. Characteristic distance is studied for single node and all nodes transmitting case when decoding is done at all intermediate nodes and only at the destination node. The results show that there is significant improvement in characteristic distance when decoding is done at all intermediate nodes. [ABSTRACT FROM AUTHOR]

The Rosenbloom–Tsfasman metric has attracted the attention of many researchers as a generalization of the Hamming metric that is relevant to practical problems. Codes for this metric were considered. In particular, Reed–Solomon codes were generalized to be compatible with this metric. In this paper, a generalization of BCH codes for the Rosenbloom–Tsfasman metric is proposed. This generalization is based on considering BCH codes as subfield subcodes of Reed–Solomon codes. By characterizing these subfield subcodes, an explicit construction of BCH codes for the Rosenbloom–Tsfasman metric is provided. Two important properties of Reed–Solomon codes and BCH codes for the Rosenbloom–Tsfasman metric are studied and compared with those for the Hamming metric. These properties are cyclic structure and duality. The approach is based on Galois-Fourier transforms associated with Hasse derivatives. [ABSTRACT FROM PUBLISHER]

In this paper, we provide methods for constructing Hermitian dual-containing (HDC) matrix-product codes over F q 2 from some non-singular matrices and a special sequence of HDC codes and determine parameters of obtained matrix-product codes when the input matrix and sequence of HDC codes satisfy some conditions. Then, using some nested HDC BCH codes with lengths n = q 4 - 1 a (a = 1 or a = q ± 1) , we construct some HDC matrix-product codes with lengths N = 2n or 3n and derive nonbinary quantum codes with length N from these matrix-product codes via Hermitian construction. Four classes of quantum codes over F q ( 3 ≤ q ≤ 5 ) are presented, whose parameters are better than those in the literature. Besides, some of our new quantum codes can exceed the quantum Gilbert-Varshamov (GV) bound. [ABSTRACT FROM AUTHOR]

Constacyclic codes are a subclass of linear codes and have been well studied. Constacyclic BCH codes are a family of constacyclic codes and contain BCH codes as a subclass. Compared with the in-depth study of BCH codes, there are relatively little study on constacyclic BCH codes. The objective of this paper is to determine the dimension and minimum distance of a class of q-ary constacyclic BCH codes of length q m − 1 q − 1 with designed distances δ i = q m − 1 − q ⌊ m − 3 2 ⌋ + i − 1 q − 1 for 1 ≤ i ≤ min { ⌈ m + 1 2 ⌉ − ⌊ m q + 1 ⌋ , ⌈ m − 1 2 ⌉ } . As will be seen, some of these codes are optimal. [ABSTRACT FROM AUTHOR]

BCH codes with efficient encoding and decoding algorithms have many applications in communications, cryptography and combinatorial design. This paper studies a class of linear codes of length q m - 1 2 over F q with special trace representation, where q is an odd prime power. With the help of the inner distributions of some subsets of association schemes of quadratic forms, we determine the weight enumerators of these codes. Determining some cyclotomic coset leaders δ i of cyclotomic cosets modulo q m - 1 2 , we prove that narrow-sense BCH codes of length q m - 1 2 with designed distance δ i = q m - q m - 1 2 - 1 - q ⌊ m - 3 2 ⌋ + i - 1 2 have the corresponding trace representation, and have the minimal distance d = δ i and the Bose distance d B = δ i , where 1 ≤ i ≤ ⌊ m + 11 6 ⌋ . [ABSTRACT FROM AUTHOR]

Unmanned aerial vehicles (UAVs) have attracted a lot of attention due to their enormous potentiality in civil and military applications over the past years. In order to allow accurate control action of UAV, a robust and real-time state estimation technique is required. In this paper, we propose a Kalman filter based UAV state estimation technique when the communication takes place over wireless links in an Internet of Things (IoT) network. We consider that a set of sensors observes the state of the UAV and transmits the observation to a control center (central server) over a distributed wireless IoT network. To deal with the communication impairments due to wireless communication links between the UAV's sensors and the IoT system components, e.g., IoT gateways, a Bose–Chaudhuri–Hocquenghem coded communication system is presented. Based on the received signals at the IoT gateways, a global state estimation technique is proposed. Performance of the proposed communication and estimation scheme is demonstrated through numerical results for different conditions. From the comparison with a conventional estimation scheme, it is observed that the proposed scheme significantly outperforms the conventional scheme in terms of state estimation and error performance. [ABSTRACT FROM AUTHOR]

Two families of new asymmetric quantum codes are constructed in this paper. The first family is the asymmetric quantum codes with length $$n=q^{m}-1$$ over $$F_{q}$$ , where $$q\ge 5$$ is a prime power. The second one is the asymmetric quantum codes with length $$n=3^{m}-1$$ . These asymmetric quantum codes are derived from the CSS construction and pairs of nested BCH codes. Moreover, let the defining set $$T_{1}=T_{2}^{-q}$$ , then the real Z-distance of our asymmetric quantum codes are much larger than $$\delta _\mathrm{max}+1$$ , where $$\delta _\mathrm{max}$$ is the maximal designed distance of dual-containing narrow-sense BCH code, and the parameters presented here have better than the ones available in the literature. [ABSTRACT FROM AUTHOR]

Very Large Scale Integration (VLSI) is the science of integrating millions of transistors in a silicon chip. It is a term describing semiconductor integrated circuits composed of thousands of logic elements of memory cells. Error occurs during the write and read operations in memory cells is a drawback for the memory ICs. Error detection and error correction plays a vital role in VLSI design by increasing the accuracy and performance of the desired circuits. Depending on the properties of the system, the channel coding can use either Automatic Repeat Request or Forward Error Correction technique in which the error correcting is introduced. In this work two techniques are used i.e. Reed Solomon code and Bose--Chaudhuri--Hocquenghem (BCH) code, where Reed Solomon code is a error detection technique which is mainly used for its possibility to adjust block length and symbol size. BCH code is a error correction technique, it is used because of its easy implementation. These two techniques are implemented in the memory cells and the performance metrics such as block length, minimum distance are calculated. From the VHDL simulation result, it is proved that BCH code is better than Reed Solomon code for the memory cells of the ICs. [ABSTRACT FROM AUTHOR]

Let q be a prime power and m a positive integer. Suppose that a ≥ 2 is a factor of q m − 1 such that m is the multiplicative order of q modulo n : = q m − 1 a. Firstly, for m odd and m even, we present some necessary and sufficient conditions on dual-containing non-primitive BCH codes of length n with the maximum designed distances over F q , respectively. The results show that the maximum designed distances of dual-containing BCH codes in this paper are larger than those in [2, Theorem 3]. Secondly, we explicitly determine the dimensions of some dual-containing non-primitive BCH codes of length n , and finally, we construct some new quantum codes with relatively large minimum distances. [ABSTRACT FROM AUTHOR]

The Bose-Chaudhuri-Hocquenghem (BCH) codes have been studied for more than 57 years and have found wide application in classical communication system and quantum information theory. In this paper, we study the construction of quantum codes from a family of q²-ary BCH codes with length n = q2m + 1 (also called antiprimitive BCH codes in the literature), where q ≥ 4 is a power of 2 and m ≥ 2. By a detailed analysis of some useful properties about q²-ary cyclotomic cosets modulo n, Hermitian dual-containing conditions for a family of non-narrowsense antiprimitive BCH codes are presented, which are similar to those of q²-ary primitive BCH codes. Consequently, via Hermitian Construction, a family of new quantum codes can be derived from these dual-containing BCH codes. Some of these new antiprimitive quantum BCH codes are comparable with those derived from primitive BCH codes. [ABSTRACT FROM AUTHOR]

The increased use of biometric-based authentication systems in a variety of applications has made biometric template protection an important issue. Unlike conventional systems, biometric cannot be revoked or changed. This made template protection a critical issue to be considered in the recent years. This paper proposes a cancelable fingerprint cryptosystem using multiple spiral curves and fuzzy commitment scheme. The method is built by combining cancelable biometrics and biometric cryptosystems. First, we compute transformed minutiae features using multiple spiral curves. Further, these transformed features are encrypted using fuzzy commitment scheme. Hence, a secure template is obtained. Experimental results and analysis prove the credibility of proposed method with recently presented methods of fingerprint template protection. [ABSTRACT FROM AUTHOR]

Maximal-entanglement entanglement-assisted quantum error-correcting codes (EAQE-CCs) can achieve the EA-hashing bound asymptotically and a higher rate and/or better noise suppression capability may be achieved by exploiting maximal entanglement. In this paper, we discussed the construction of quaternary zero radical (ZR) codes of dimension five with length . Using the obtained quaternary ZR codes, we construct many maximal-entanglement EAQECCs with very good parameters. Almost all of these EAQECCs are better than those obtained in the literature, and some of these EAQECCs are optimal codes. [ABSTRACT FROM AUTHOR]

In this paper, we firstly study construction of new quantum error-correcting codes (QECCs) from three classes of quaternary imprimitive BCH codes. As a result, the improved maximal designed distance of these narrow-sense imprimitive Hermitian dual-containing quaternary BCH codes are determined to be much larger than the result given according to Aly et al. (IEEE Trans Inf Theory 53:1183-1188, 2007) for each different code length. Thus, families of new QECCs are newly obtained, and the constructed QECCs have larger distance than those in the previous literature. Secondly, we apply a combinatorial construction to the imprimitive BCH codes with their corresponding primitive counterpart and construct many new linear quantum codes with good parameters, some of which have parameters exceeding the finite Gilbert-Varshamov bound for linear quantum codes. [ABSTRACT FROM AUTHOR]

For digital images, many watermarking schemes regarding copyright issue have been proposed. However, there exist many attacks trying to break or remove the embedded watermark. Therefore, the embedded watermark should be robust against all kinds of attacks. Among various attacks, the print and scan (PS) attack is a challenging one because it not only alters the pixel values but also changes the positions of original pixels. Most of the existing watermarking systems would fail under such an attack. In this paper, a watermarking system operating in the discrete cosine transform domain is proposed for colour images. By efficiently integrating the three components, red, green and blue, the proposed system exhibits superior robustness against various attacks, including the PS attack. According to the simulation results, the system maintains an acceptable image quality while providing outstanding robustness against the PS attack. [ABSTRACT FROM AUTHOR]

Bose-Chaudhuri-Hocquenghem (BCH) codes have been intensively investigated. Even so, there is only a little known about primitive BCH codes, let alone non-primitive ones. In this paper, let q > 2 be a prime power, the dimension of a family of non-primitive BCH codes of length n = q m + 1 (also called antiprimitive) is studied. These codes are also linear codes with complementary duals (called LCD codes). Through some approaches such as iterative algorithm, partition and scaling, all coset leaders of C x modulo n with q ⌈ m 2 ⌉ < x ≤ 2 q ⌈ m 2 ⌉ + 2 are given for m ≥ 4. And for odd m the first several largest coset leaders modulo n are determined. Furthermore, a new kind of sequences is introduced to determine the second largest coset leader modulo n with m even and q odd. Also, for even m some conjectures about the first several coset leaders modulo n are proposed, whose complete verification would wipe out the difficult problem to determine the first several coset leaders of antiprimitive BCH codes. After deriving the cardinalities of the coset leaders, we shall calculate exact dimensions of many antiprimitive LCD BCH codes. [ABSTRACT FROM AUTHOR]

BCH codes are an important class of cyclic codes, and have wide applications in communication and storage systems. However, it is difficult to determine the parameters of BCH codes and only a few cases are known. In this paper, we mainly study three classes of BCH codes with n = q m − 1 , q 2 s − 1 q + 1 , q m − 1 q − 1. On one hand, we provide the parameters of C (n , q , δ , 1) and its dual code in some cases. On the other hand, we provide the sufficient and necessary conditions to guarantee that C (n , q , δ , 2) is a dually-BCH code. [ABSTRACT FROM AUTHOR]

In this paper, narrow-sense and non-narrow-sense BCH codes of length n =2(q4−1) that contain their Hermitian duals over Fq2 are studied, where q is an odd prime power. Theory of cyclotomic coset is applied to confirm the maximum designed distances and dimensions of these BCH codes. Finally, some new quantum codes are obtained from such BCH codes, many of our quantum codes are much better than those from narrow-sense BCH codes in [12]. [ABSTRACT FROM AUTHOR]