Minimal linear codes from defining sets over Fp plus uFp

被引：1

作者：

Gao, Jian ^{[1
]}

Zhang, Yaozong ^{[1
]}

Meng, Xiangrui ^{[2
,3
]}

Fu, Fang-Wei ^{[2
,3
]}

机构：

[1] Shandong Univ Technol, Sch Math & Stat, Zibo 255091, Peoples R China

[2] Nankai Univ, Chern Inst Math, Tianjin 300071, Anguilla

[3] Nankai Univ, Tianjin Key Lab Network & Data Secur Technol, LPMC, Tianjin 300071, Peoples R China

来源：

DISCRETE MATHEMATICS | 2023年 / 346卷 / 10期

基金：

中国国家自然科学基金;

关键词：

Linear codes; Exponential sums; Lee-weight distributions; Complete weight enumerator; Minimal linear codes; COMPLETE WEIGHT ENUMERATORS; FINITE-FIELDS; CYCLIC CODES; 3-WEIGHT; 2-WEIGHT; CONSTRUCTION; FAMILIES;

D O I：

10.1016/j.disc.2023.113584

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Minimal codes are a special type of linear codes, which have nice applications in secret sharing and secure two-party computation. How to construct new infinite family of minimal codes has been a hot topic in coding theory and cryptography. In this paper, by employing exponential sums, we study the Lee-weight distributions of several classes of linear codes from defining sets over the finite chain ring Fp + uFp and determine exactly the complete weight enumerator of their Gray images under the Gray map. Furthermore, we prove that the Gray images of these linear codes are new infinite families of minimal five-weight linear codes with wmin wmax < p-1 p . & COPY; 2023 Elsevier B.V. All rights reserved.

引用

页数：18

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