MDS constacyclic codes of length q+1 over GF(q)

被引：3
作者：
Wang, Xiaoqiang [1 ]
Ding, Cunsheng [2 ]
Liu, Hongwei [3 ]
Zheng, Dabin [1 ]
机构：
[1] Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, Wuhan 430062, Peoples R China
[2] Hong Kong Univ Sci & Technol, Dept Comp Sci & Engn, Kowloon, Clear Water Bay, Hong Kong, Peoples R China
[3] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China
来源：
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES | 2024年 / 16卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Constacyclic code; Cryptography; Cyclic code; Linear code; MDS code;
D O I：
10.1007/s12095-022-00624-0
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
MDS constacyclic codes over finite fields are important in both theory and practice. In this paper, all [q + 1,2,q] and [q + 1,3,q - 1] MDS lambda-constacyclic codes over GF(q) are characterized, three classes of [q + 1,4,q - 2] MDS lambda-constacyclic codes over GF(q) are constructed, and four classes of [q + 1,k,q - k + 2] MDS lambda-constacyclic codes over GF(q) for variable k are presented. Rationales for distinguishing the class of cyclic codes, the class of lambda-constacyclic codes with lambda not equal 1, and the class of non-constacyclic linear codes are given. Some applications of MDS codes in cryptography are also summarised.
引用
收藏
页码：21 / 48
页数：28
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