Search

Let I be the commutative non-unital ring of order 4 defined by generators and relations. I = a , b ∣ 2 a = 2 b = 0 , a 2 = b , a b = 0. Alahmadi et al. have classified QSD codes, Type IV codes (QSD codes with even weights) and quasi-Type IV codes (QSD codes with even torsion code) over I up to lengths n = 6 , and suggested two building-up methods for constructing QSD codes. In this paper, we construct more QSD codes, Type IV codes and quasi-Type IV codes for lengths n = 7 and 8, and describe five new variants of the two building-up construction methods. We find that when n = 8 there is at least one QSD code with minimun distance 4, which attains the highest minimum distance so far, and we give a generator matrix for the code. We also describe some QSD codes, Type IV codes and quasi-Type IV codes with new weight distributions. [ABSTRACT FROM AUTHOR]

Teaching outdoors is an obligatory part of physical education (PE) in most countries; therefore, PE holds great potential to contribute to learning about nature, the environment and environmental sustainability (ES). This paper reports the investigation of whether Swedish PE teachers perceive ES as part of their subject, and if so, how do they implement it? Drawing on 60 PE teachers’ answers to five opened questions (53 written answers and 7 oral interviews), and using British sociologist Basil Bernstein’s concepts of classification and codes, this study have asked the following research questions: 1. What influences the position and legitimisation of ES in PE? 2. How does the subject culture of Swedish PE influence the introduction of ES? The result from the study shows a complexity regarding the strength of the boundaries that surround ES in PE and what this complexity might offer in terms of enablers and constraints. The result also displays a strong connection between outdoor education and its potential for teaching ES. Various options are discussed with regard to where (in what content areas in PE) and how to implement ES. [ABSTRACT FROM AUTHOR]

Due to the increasing complexity of modern integrated circuits, high-level synthesis (HLS) is becoming a key technology in hardware design. HLS uses optimizations to assist during design space exploration. However, some of them can introduce security weaknesses. We propose an approach that leverages static analysis to identify a class of weaknesses in HLS-generated code. We show that some of these weaknesses can be corrected through the automatic generation of HLS directives. We evaluate our approach by comparing the static analysis results with formal verification. Our results show that the static approach has the same accuracy as formal methods while being $3\times $ to $200\times $ faster. [ABSTRACT FROM AUTHOR]

In this paper, we introduce some new polynomials associated to linear codes over F q. In particular, we introduce the notion of split complete Jacobi polynomials attached to multiple sets of coordinate places of a linear code over F q , and give the MacWilliams type identity for it. We also give the notion of generalized q -colored t -designs. As an application of the generalized q -colored t -designs, we derive a formula that obtains the split complete Jacobi polynomials of a linear code over F q. Moreover, we define the concept of colored packing (resp. covering) designs. Finally, we give some coding theoretical applications of the colored designs for Type III and Type IV codes. [ABSTRACT FROM AUTHOR]

We consider the problem of constructing prefix-free codes in which a designated symbol, a space, can only appear at the end of codewords. We provide a linear-time algorithm to construct almost-optimal codes with this property, meaning that their average length differs from the minimum possible by at most one. We obtain our results by uncovering a relation between our class of codes and the class of one-to-one codes. Additionally, we derive upper and lower bounds to the average length of optimal prefix-free codes with a space in terms of the source entropy. [ABSTRACT FROM AUTHOR]

This letter proposes an augmented scheme of LT codes to improve the decoding success rate. The method involves substituting the 1‐s in full‐degree columns of the generator matrix of conventional LT codes with binary extension field elements and simultaneously increasing the ratio of full‐degree columns in the ideal soliton distribution. For non‐full‐degree columns, we retain the nonzero elements as 1‐s in the conventional LT codes generator matrix to preserve computational efficiency. Compared to conventional LT codes, the proposed method enhances the linear independence of the generator matrix, leading to a higher decoding success rate with minimal data packets. Experimental results demonstrate the effectiveness of the method at improving the performance of LT codes, with close to 100% decoding success rate achieved with around 5% data redundancy. [ABSTRACT FROM AUTHOR]

Currently, the study of energy balancing in cascaded multilevel inverter cells is desirable due to the growing interest in implementing systems that minimize losses, ensure delivery of the maximum amount of power to the load, contribute to system reliability, and at the same time minimize the use of resources for its implementation. One of the ways to carry out energy balancing without resorting to additional topology is by modifying conventional modulation techniques. In this letter, the FPGA implementation of modulation strategies for energy balancing purposes is carried out. First, three conventional techniques are addressed: 1) phase-shifted carrier disposition; 2) level shift per carrier cycle; and 3) level shift per modulator cycle. Subsequently, the implementation of an alternative modulation strategy that performs energy balancing in the cascaded multilevel inverter, minimizing the use of digital resources, is presented. [ABSTRACT FROM AUTHOR]

Adverse life events have short- and long-term effects on the livelihood of victims. This paper studies the effect of early life idiosyncratic shocks on labour market outcomes using five rounds of panel data from the National Income Dynamics Study (NIDS) of South Africa. Regression results from alternative panel data estimators suggest that the loss of biological parents early in life is negatively associated with the likelihood of employment and wage earnings. The association is stronger when one loses one's biological mother than one's biological father. Heterogeneity analysis reveals that the loss of a biological father among Black South Africans leads to higher wage earnings compared to other race groups who have experienced the same shock. Education level, perceived health, cognitive ability, and occupation type are strongly associated with the loss of a biological mother, while only education is associated with the loss of a father. These could be the main channels that mediate the link between early life loss of biological parents and labour market outcomes. Therefore, strengthening and aligning child support programmes to reach the victims are required.

A lower bound is presented for the minimal number of filled cells in a maximal partial Latin hypercube of dimension d and order n. The result generalises and extends previous results for d = 2 (Latin squares) and d = 3 (Latin cubes). Explicit constructions show that this bound is near-optimal for large n > d . For d > n , a connection with Hamming codes shows that this lower bound gives a related upper bound for the same quantity. The results can be interpreted in terms of independent dominating sets in certain graphs, and in terms of codes that have covering radius 1 and minimum distance at least 2. [ABSTRACT FROM AUTHOR]

Quantum computers have the potential to provide exponential speedups over their classical counterparts. Quantum principles are being applied to fields such as communications, information processing, and artificial intelligence to achieve quantum advantage. However, quantum bits are extremely noisy and prone to decoherence. Thus, keeping the qubits error free is extremely important toward reliable quantum computing. Quantum error correcting codes have been studied for several decades and methods have been proposed to import classical error correcting codes to the quantum domain. Along with the exploration into novel and more efficient quantum error correction codes, it is also essential to design circuits for practical realization of these codes. This article serves as a tutorial on designing and simulating quantum encoder and decoder circuits for stabilizer codes. We first describe Shor’s 9-qubit code which was the first quantum error correcting code. We discuss the stabilizer formalism along with the design of encoding and decoding circuits for stabilizer codes such as the five-qubit code and Steane code. We also design nearest neighbor compliant circuits for the above codes. The circuits were simulated and verified using IBM Qiskit. [ABSTRACT FROM AUTHOR]