Constructions of several classes of linear codes with a few weights

被引：1
|
作者：
Liu, Hongwei [1 ]
Ouyang, Jianxin [1 ,2 ]
Wang, Xiaoqiang [3 ]
机构：
[1] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China
[2] Guizhou Educ Univ, Sch Math & Big Data, Guiyang 550018, Peoples R China
[3] Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, Wuhan 430062, Peoples R China
来源：
DISCRETE MATHEMATICS | 2020年 / 343卷 / 12期
关键词：
Linear code; Weight distribution; Gauss sum; MDS code; Optimal code; 3-WEIGHT CODES; 2-WEIGHT;
D O I：
10.1016/j.disc.2020.112108
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Recently, linear codes with a few weights have been constructed and extensively studied due to their applications in secret sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, we construct several classes of linear codes with a few weights over IFp, where p is an odd prime. The weight distributions of these constructed codes are also settled by applications of the theory of quadratic forms and Gauss sums over finite fields. Some of the linear codes obtained are optimal or almost optimal. The parameters of these linear codes are new in most cases. Moreover, two classes of MDS codes are obtained. (c) 2020 Elsevier B.V. All rights reserved.
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页数：20
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