Related papers: On the Weight Distribution of Concatenated Code En…
Currently known secondary construction techniques for linear codes mainly include puncturing, shortening, and extending. In this paper, we propose a novel method for the secondary construction of linear codes based on their weight…
Interleaved Reed-Solomon codes are applied in numerous data processing, data transmission, and data storage systems. They are generated by interleaving several codewords of ordinary Reed-Solomon codes. Usually, these codewords are decoded…
The study of the generalized Hamming weight of linear codes is a significant research topic in coding theory as it conveys the structural information of the codes and determines their performance in various applications. However,…
In 2021, Augot, Couvreur, Lavauzelle and Neri introduced a new class of rank metric codes which can be regarded as rank metric counterparts of Reed-Muller codes. Given a finite Galois extension $\mathbb{L} / \mathbb{K}$, these codes are…
Let R > S be finite Frobenius rings for which there exists a trace map T from R onto S as left S modules. Let C:= {x -> T(ax + bf(x)) : a,b in R}. Then C is an S-linear subring-subcode of a left linear code over R. We consider functions f…
Usually, it is difficult to determine the weight distribution of an irreducible cyclic code. In this paper, we discuss the case when an irreducible cyclic code has the maximal number of distinct nonzero weights and give a necessary and…
Linear codes with few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of…
We use the relations between quadrics, trace codes and algebraic curves to construct algebraic curves over finite fields with many points and to compute generalized Hamming weights of codes.
Multiplex networks describe a large number of systems ranging from social networks to the brain. These multilayer structure encode information in their structure. This information can be extracted by measuring the correlations present in…
Code Division Multiple Access (CDMA) in which the spreading code assignment to users contains a random element has recently become a cornerstone of CDMA research. The random element in the construction is particular attractive as it…
Irreducible cyclic codes are one of the largest known classes of block codes which have been investigated for a long time. However, their weight distributions are known only for a few cases. In this paper, a class of irreducible cyclic…
This paper presents a generalization of the random dot product model for networks whose edge weights are drawn from a parametrized probability distribution. We focus on the case of integer weight edges and show that many previously studied…
We calculate the probability (``quenching weight'') that a hard parton radiates an additional energy fraction due to scattering in spatially extended QCD matter. This study is based on an exact treatment of finite in-medium path length, it…
The duals of cyclic codes with two zeros have been extensively studied, and their weight distributions have recently been evaluated in some cases. In this note, we determine the weight distribution of a certain new class of such codes by…
A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…
This paper introduces a new combinatorial construction for q-ary constant-weight codes which yields several families of optimal codes and asymptotically optimal codes. The construction reveals intimate connection between q-ary…
Coded computing is a distributed paradigm that uses coding theory to introduce \textit{redundancy} and overcome bottlenecks in large-scale systems. In the same vein, randomized numerical linear algebra employs probabilistic methods to…
It is well-known that Reed-Solomon codes and extended Reed-Solomon codes are two special classes of MDS codes with wide applications in practice. The complete weight enumerators of these codes are very important for determining the…
Weight-ensembles are formed when the parameters of multiple neural networks are directly averaged into a single model. They have demonstrated generalization capability in-distribution (ID) and out-of-distribution (OOD) which is not…
The Muttalib-Borodin ensemble is a probability density function for $n$ particles on the positive real axis that depends on a parameter $\theta$ and a weight $w$. We consider a varying exponential weight that depends on an external field…