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In this paper, for an odd prime $p$, by extending Li et al.'s construction \cite{CL2016}, several classes of two-weight and three-weight linear codes over the finite field $\mathbb{F}_p$ are constructed from a defining set, and then their…

Information Theory · Computer Science 2021-07-07 Canze Zhu , Qunying Liao

Linear codes with a few weights can be applied to secrete sharing, authentication codes, association schemes and strongly regular graphs. For an odd prime power $q$, we construct a class of three-weight $\F_q$-linear codes from quadratic…

Information Theory · Computer Science 2024-10-04 Xiumei Li , Zongxi Chen , Fei Li

In the past few years, linear codes with few weights and their weight analysis have been widely studied. In this paper, we further investigate a class of two-weight or three-weight linear codes from defining sets and determine their weight…

Information Theory · Computer Science 2020-09-11 Dabin Zheng , Qing Zhao , Xiaoqiang Wang , Yan Zhang

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…

Information Theory · Computer Science 2016-01-27 Xiaoni Du , Yunqi Wan

In this paper, based on the theory of defining sets, a class of four-weight or five-weight linear codes over Fp is constructed. The complete weight enumerators of the linear codes are determined by means of Weil sums. In some case, there is…

Information Theory · Computer Science 2020-12-10 Xina Zhang

We construct a class of linear codes by choosing a proper defining set and determine their complete weight enumerators and weight enumerators. The results show that they are at most three-weight codes and they are suitable for applications…

Information Theory · Computer Science 2019-01-23 Shudi Yang , Xiangli Kong

Recently, linear codes with few weights have been constructed and extensively studied. In this paper, for an odd prime p, we determined the complete weight enumerator of two classes of p-ary linear codes constructed from defining set.…

Information Theory · Computer Science 2015-12-24 Qiuyan Wang , Fei Li , Kelan Ding , Dongdai Lin

Linear codes have been an interesting topic in both theory and practice for many years. In this paper, for an odd prime $p$, we determine the explicit complete weight enumerators of two classes of linear codes over $\mathbb{F}_p$ and they…

Information Theory · Computer Science 2015-07-21 Shudi Yang , Zheng-An Yao

Linear codes have been an interesting topic in both theory and practice for many years. In this paper, for an odd prime $p$, we present the explicit complete weight enumerator of a family of $p$-ary linear codes constructed with defining…

Information Theory · Computer Science 2017-07-07 Shudi Yang , Zheng-An Yao

Recently, linear codes constructed from defining sets have been studied extensively. They may have nice parameters if the defining set is chosen properly. Let $ m >2$ be a positive integer. For an odd prime $ p $, let $ r=p^m $ and…

Information Theory · Computer Science 2017-04-10 Shudi Yang , Xiangli Kong , Chunming Tang

Recently, linear codes constructed from defining sets have been investigated extensively and they have many applications. In this paper, for an odd prime $p$, we propose a class of $p$-ary linear codes by choosing a proper defining set.…

Information Theory · Computer Science 2017-07-07 Shudi Yang , Zheng-An Yao , Chang-An Zhao

In this article, we show explicitly all possible weight enumerators for every irreducible cyclic code of length $n$ over a finite field $\mathbb F_q$, in the case which each prime divisor of $n$ is also a divisor of $q-1$.

Information Theory · Computer Science 2014-05-12 F. E. Brochero Martínez , C. R. Giraldo Vergara

We study the generalized and extended weight enumerator of the q-ary Simplex code and the q-ary first order Reed-Muller code. For our calculations we use that these codes correspond to a projective system containing all the points in a…

Combinatorics · Mathematics 2017-10-24 Relinde Jurrius

Linear codes with few weights have applications in secret sharing, authentication codes, association schemes and strongly regular graphs. In this paper, several classes of $t$-weight linear codes over ${\mathbb F}_{q}$ are presented with…

Information Theory · Computer Science 2025-01-22 Zhao Hu , Mingxiu Qiu , Nian Li , Xiaohu Tang , Liwei Wu

Linear codes with a few weights have important applications in authentication codes, secret sharing, consumer electronics, etc.. The determination of the parameters such as Hamming weight distributions and complete weight enumerators of…

Information Theory · Computer Science 2017-11-15 Minglong Qi , Shengwu Xiong , Jingling Yuan , Wenbi Rao , Luo Zhong

Linear codes can be employed to construct authentication codes, which is an interesting area of cryptography. The parameters of the authentication codes depend on the complete weight enumerator of the underlying linear codes. In order to…

Information Theory · Computer Science 2015-05-27 Can Xiang , Hao Liu

In this paper, we discuss the generalized Hamming weights of a class of linear codes associated with non-degenerate quadratic forms. In order to do so, we study the quadratic forms over subspaces of finite field and obtain some interesting…

Information Theory · Computer Science 2021-06-08 Fei Li

Recently, linear codes with a few weights were widely investigated due to their applications in secret sharing schemes and authentication schemes. In this letter, we present a class of $q$-ary linear codes derived from irreducible cyclic…

Information Theory · Computer Science 2016-04-18 Ziling Heng , Qin Yue

For any q which is a power of 2 we describe a finite subgroup of the group of invertible complex q by q matrices under which the complete weight enumerators of generalized doubly-even self-dual codes over the field with q elements are…

Number Theory · Mathematics 2014-09-17 Gabriele Nebe , H. -G. Quebbemann , E. M. Rains , N. J. A. Sloane

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…

Combinatorics · Mathematics 2007-07-16 I. M. Duursma , M. Greferath
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