Related papers: Linear codes with few weights from non-weakly regu…
In this paper, we present a construction of linear codes over $\f_{2^t}$ from Boolean functions, which is a generalization of Ding's method \cite[Theorem 9]{Ding15}. Based on this construction, we give two classes of linear codes…
We first establish a simple yet powerful necessary and sufficient condition for a binary linear code to be SO, leading to a complete characterization of singly-even codes in this family. We further derive necessary and sufficient conditions…
We provide a combinatorial construction for linear codes attaining the maximum possible number of distinct weights. We then introduce the related problem of determining the existence of linear codes with an arbitrary number of distinct…
In this paper, for any odd prime $p$ and an integer $m\ge 3$, several classes of linear codes with $t$-weight $(t=3,5,7)$ are obtained based on some defining sets, and then their complete weight enumerators are determined explicitly by…
In this paper, on one hand, a class of linear codes with one or two weights is obtained. Based on these linear codes, we construct two classes of constant composition codes, which includes optimal constant composition codes depending on…
As a special class of linear codes, minimal linear codes have important applications in secret sharing and secure two-party computation. Constructing minimal linear codes with new and desirable parameters has been an interesting research…
Recently some mixed alphabet rings are involved in constructing few-Lee weight additive codes with optimal or minimal Gray images using suitable defining sets or down-sets. Inspired by these works, we choose the mixed alphabet ring…
The weight distribution and weight hierarchy of a linear code are two important research topics in coding theory. In this paper, choosing $ D=\Big\{(x,y)\in \Big(\F_{p^{s_1}}\times\F_{p^{s_2}}\Big)\Big\backslash\{(0,0)\}:…
In recent years, there have been many constructions of minimal linear codes violating the Ashikhmin-Barg condition from Boolean functions, linear codes with few nonzero weights or partial difference sets. In this paper, we first give a…
Recently, much progress has been made to construct minimal linear codes due to their preference in secret sharing schemes and secure two-party computation. In this paper, we put forward a new method to construct minimal linear codes by…
The study on minimal linear codes has received great attention due to their significant applications in secret sharing schemes and secure two-party computation. Until now, numerous minimal linear codes have been discovered. However, to the…
Linear codes with a few weights have been widely investigated in recent years. In this paper, we mainly use Gauss sums to represent the Hamming weights of a class of $q$-ary linear codes under some certain conditions, where $q$ is a power…
Based on a generic construction, two classes of ternary three-weight linear codes are obtained from a family of power functions, including some APN power functions. The weight distributions of these linear codes are determined through…
Boolean functions can be used to construct binary linear codes in many ways, and vice versa. The objective of this short article is to point out a connection between the weight distributions of all projective binary linear codes and the…
There are several methods for constructing secret sharing schemes, one of which is based on coding theory. Theoretically, every linear code can be used to construct secret sharing schemes. However, in general, determining the access…
Linear codes are widely studied in coding theory as they have nice applications in distributed storage, combinatorics, lattices, cryptography and so on. Constructing linear codes with desirable properties is an interesting research topic.…
Minimal linear codes have interesting applications in secret sharing schemes and secure two-party computation. This paper uses characteristic functions of some subsets of $\mathbb{F}_q$ to construct minimal linear codes. By properties of…
Linear codes have been an interesting topic in both theory and practice for many years. In this paper, for an odd prime power $q$, we construct some class of linear code over finite field $\mathbb{F}_q$ with defining set be the preimage of…
Recently, minimal linear codes have been extensively studied due to their applications in secret sharing schemes, secure two-party computations, and so on. Constructing minimal linear codes violating the Ashikhmin-Barg condition and then…
We introduce a consistent and efficient method to construct self-dual codes over $GF(q)$ with symmetric generator matrices from a self-dual code over $GF(q)$ of smaller length where $q \equiv 1 \pmod 4$. Using this method, we improve the…