Several families of irreducible constacyclic and cyclic codes

被引：3

作者：

Sun, Zhonghua ^{[1
]}

Wang, Xiaoqiang ^{[2
]}

Ding, Cunsheng ^{[3
]}

机构：

[1] Hefei Univ Technol, Sch Math, Hefei 230601, Anhui, Peoples R China

[2] Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, Wuhan 430062, Hubei, Peoples R China

[3] Hong Kong Univ Sci & Technol, Dept Comp Sci & Engn, Kowloon, Clear Water Bay, Hong Kong, Peoples R China

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2023年 / 91卷 / 9期

基金：

中国国家自然科学基金;

关键词：

Constacyclic code; Irreducible constacyclic code; Irreducible cyclic code; Weight distribution; WEIGHT DISTRIBUTIONS; HAMMING WEIGHTS;

D O I：

10.1007/s10623-023-01242-4

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper, several families of irreducible constacyclic codes over finite fields and their duals are studied. The weight distributions of these irreducible constacyclic codes and the parameters of their duals are settled. Several families of irreducible constacyclic codes with a few weights and several families of optimal constacyclic codes are constructed. As byproducts, a family of [2n, (n -1)/2, d = 2(vn+1)] irreducible cyclic codes over GF((q)) and a family of [(q-1)n, (n-1)/2,d =(q-1)(vn+1)] irreducible cyclic codes over GF((q)) are presented, where n is a prime such that ord(2n)(q) = (n - 1)/2 and ord((q-1)n)(q) = (n - 1)/2, respectively. The results in this paper complement earlier works on irreducible constacyclic and cyclic codes over finite fields.

引用

页码：2821 / 2843

页数：23

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