Repeated-root constacyclic codes of length p1pt2ps and their dual codes

被引：2

作者：

Wu, Hongfeng ^{[1
]}

Zhu, Li ^{[2
]}

机构：

[1] North China Univ Technol, Coll Sci, Beijing 100144, Peoples R China

[2] Guizhou Univ, Sch Math & Stat, Guiyang 550025, Peoples R China

来源：

AIMS MATHEMATICS | 2023年 / 8卷 / 06期

关键词：

finite fields; cyclic codes; constacyclic codes; cyclotomic cosets; dual code;

D O I：

10.3934/math.2023644

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let liq be the finite field with q = pk elements, and p1, p2 be two distinct prime numbers different from p. In this paper, we first calculate all the q-cyclotomic cosets modulo p1pt2 as a preparation for the following parts. Then we give the explicit generator polynomials of all the constacyclic codes of length p1 pt2ps over liq and their dual codes. In the rest of this paper, we determine all self-dual cyclic codes of length p1 pt2 ps and their enumeration. This answers a question recently asked by B. Chen, H.Q.Dinh and Liu. In the last section, we calculate the case of length 5europs as an example.

引用

页码：12793 / 12818

页数：26

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