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

共 50 条

[41] A class of constacyclic codes over Fp plus vFp and its Gray image
Zhu, Shixin
Wang, Liqi
DISCRETE MATHEMATICS, 2011, 311 (23-24) : 2677 - 2682
[42] Cyclic codes and λ1 + λ2u + λ3v + λ4uv-constacyclic codes over Fp + uFp + vFp + uvFp
Zheng, Xiying
Kong, Bo
APPLIED MATHEMATICS AND COMPUTATION, 2017, 306 : 86 - 91
[43] Linear codes from defining sets over Fp+uFp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {F}}_{p} +u{\mathbb {F}}_{p}$$\end{document} and their applications
Xiangdi Zeng
Yaozong Zhang
Jian Gao
Computational and Applied Mathematics, 2024, 43 (1)
[44] GOOD p-ARY QUASIC-CYCLIC CODES FROM CYCLIC CODES OVER Fp + νFp
Shi, Minjia
Yang, Shanlin
Zhu, Shixin
JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY, 2012, 25 (02) : 375 - 384
[45] Minimal Linear Codes Constructed from Sunflowers
Wu, Xia
Lu, Wei
Alcaraz, Raul
ENTROPY, 2023, 25 (12)
[46] Minimal linear codes constructed from functions
Xia Wu
Wei Lu
Xiwang Cao
Cryptography and Communications, 2022, 14 : 875 - 895
[47] On Hamming Distance Distributions of Repeated-Root Cyclic Codes of Length 5ps Over Fp m + uFp m
Dinh, Hai Q.
Nguyen, Bac T.
Thi, Hiep L.
Yamaka, Woraphon
IEEE ACCESS, 2022, 10 : 119883 - 119904
[48] Optimal minimal linear codes from posets
Hyun, Jong Yoon
Kim, Hyun Kwang
Wu, Yansheng
Yue, Qin
DESIGNS CODES AND CRYPTOGRAPHY, 2020, 88 (12) : 2475 - 2492
[49] Optimal minimal linear codes from posets
Jong Yoon Hyun
Hyun Kwang Kim
Yansheng Wu
Qin Yue
Designs, Codes and Cryptography, 2020, 88 : 2475 - 2492
[50] Minimal Linear Codes From Characteristic Functions
Mesnager, Sihem
Qi, Yanfeng
Ru, Hongming
Tang, Chunming
IEEE TRANSACTIONS ON INFORMATION THEORY, 2020, 66 (09) : 5404 - 5413

← 1 2 3 4 5 →