On constacyclic codes of length 9ps over Fpm and their optimal codes

被引：0

作者：

Dinh, Hai Q. ^{[1
]}

Ha, Hieu V. ^{[2
,3
]}

Nguyen, Nhan T. V. ^{[4
]}

Tran, Nghia T. H. ^{[5
]}

机构：

[1] Kent State Univ, Dept Math Sci, Kent, OH 44483 USA

[2] Univ Econ & Law, Fac Econ Math, Ho Chi Minh City, Vietnam

[3] Vietnam Natl Univ, Ho Chi Minh City, Vietnam

[4] Lawrence S Ting Sch, Ho Chi Minh City, Vietnam

[5] Ho Chi Minh City Univ Educ, Dept Math, Ho Chi Minh City, Vietnam

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2024年 / 23卷 / 08期

关键词：

Hamming distance; repeated-root constacyclic code; cyclic code; MDS code; AMDS code; near-MDS code; CYCLIC CODES; DISTANCE;

D O I：

10.1142/S0219498825500768

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The problem of classifying constacyclic codes over a finite field, both the Hamming distance and the algebraic structure, is an interesting problem in algebraic coding theory. For the repeated-root constacyclic codes of length np(s) over F-pm, where p is a prime number and p does not divide n, the problem has been solved completely for all n <= 6 and partially for n = 7, 8. In this paper, we solve the problem for n = 9 and all primes p different from 3 and 19. In particular, we characterize the Hamming distance of all repeated-root constacyclic codes of length 9p(s) over F-pm. As an application, we identify all optimal and near-optimal codes with respect to the Singleton bound of these types, namely, MDS, almost-MDS, and near-MDS codes.

引用

页数：42

共 22 条

[1] ON REPEATED-ROOT CYCLIC CODES [J].