Related papers: Complete weight enumerators of two classes of line…
Linear codes with few weights have significant applications in secret sharing schemes, authentication codes, association schemes, and strongly regular graphs. There are a number of methods to construct linear codes, one of which is based on…
Linear codes with few weights have applications in secret sharing, authentication codes, association schemes and strongly regular graphs. In this paper, several classes of two-weight and three-weight linear codes are presented and their…
Three classes of binary linear codes with at most four nonzero weights were constructed in this paper, in which two of them are projective three-weight codes. As applications, $s$-sum sets for any odd $ s > 1$ were constructed.
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,…
Projective two-weight linear codes are closely related to finite projective spaces and strongly regular graphs. In this paper, a family of $q$-ary projective two-weight linear codes is presented, where $q$ is a power of 2. The parameters of…
We express the weight enumerators of self-dual and doubly even (Type II for short) codes of length $24$ with a specified basis. As a consequence, we present some congruence relations among the weight enumerators.
The paper describes a method to determine symmetrized weight enumerators of $p^m$-linear codes based on the notion of a disjoint weight enumerator. Symmetrized weight enumerators are given for the lifted quadratic residue codes of length 24…
The determination of the weight distribution of linear codes has been a fascinating problem since the very beginning of coding theory. There has been a lot of research on weight enumerators of special cases, such as self-dual codes and…
In this paper, we give a representation of the average of complete joint weight enumerators of two linear codes of length $n$ over $\mathbb{F}_{q}$ and $\mathbb{Z}_{k}$ in terms of the compositions of $n$ and their distributions in the…
Studying the generalized Hamming weights of linear codes is a significant research area within coding theory, as it provides valuable structural information about the codes and plays a crucial role in determining their performance in…
Cyclic codes are an important class of linear codes, whose weight distribution have been extensively studied. So far, most of previous results obtained were for cyclic codes with no more than three zeros. Recently, \cite{Y-X-D12}…
Linear codes with few weights have applications in authentication codes, secrete sharing schemes, association schemes, consumer electronics and data storage system. In this paper, several classes of linear codes with two or three weights…
Linear codes are the most important family of codes in cryptography and coding theory. Some codes have only a few weights and are widely used in many areas, such as authentication codes, secret sharing schemes and strongly regular graphs.…
In this study, linear codes having their Lee-weight distributions over the semi-local ring $\mathbb{F}_{q}+u\mathbb{F}_{q}$ with $u^{2}=1$ are constructed using the defining set and Gauss sums for an odd prime $q $. Moreover, we derive…
Self-orthogonal codes are a significant class of linear codes in coding theory and have attracted a lot of attention. In \cite{HLL2023Te,LH2023Se}, $p$-ary self-orthogonal codes were constructed by using $p$-ary weakly regular bent…
In this paper, several classes of three-weight codes and two-weight codes for the homogeneous metric over the chain ring $R=\mathbb{F}_p+u\mathbb{F}_p+\cdots +u^{k-1}\mathbb{F}_{p},$ with $u^k=0,$ are constructed, which generalises…
In this paper, several classes of three-weight codes and two-weight codes for the homogeneous metric over the chain ring $R=\mathbb{F}_p+u\mathbb{F}_p+\cdots +u^{k-1}\mathbb{F}_{p},$ with $u^k=0,$ are constructed, which generalises…
In this paper we present a new method for finding the weight enumerator of binary linear block codes by using genetic algorithms. This method consists in finding the binary weight enumerator of the code and its dual and to create from the…
The existence of optimal binary self-dual codes is a long-standing research problem. In this paper, we present some results concerning the decomposition of binary self-dual codes with a dihedral automorphism group $D_{2p}$, where $p$ is a…
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…