Hamming distances of constacyclic codes of length 3ps and optimal codes with respect to the Griesmer and Singleton bounds

被引:2
作者
Dinh, Hai Q. [1 ,3 ]
Wang, Xiaoqiang [2 ]
Liu, Hongwei [4 ]
Yamaka, Woraphon [5 ]
机构
[1] Ton Duc Thang Univ, Inst Computat Sci, Div Computat Math & Engn, Ho Chi Minh City, Vietnam
[2] Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, Wuhan 430062, Peoples R China
[3] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam
[4] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China
[5] Chiang Mai Univ, Fac Econ, Ctr Excellence Econometr, Chiang Mai 52000, Thailand
基金
中国国家自然科学基金;
关键词
Constacyclic code; Repeated-root code; Hamming distance; Griesmer bound; Singleton bound; ROOT CYCLIC CODES;
D O I
10.1016/j.ffa.2020.101794
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let p not equal 3 be a prime, s, in be positive integers, and A be a nonzero element of the finite field F-pm . In [22] and [20], when the generator polynomials have one or two different irreducible factors, the Hamming distances of lambda-constacyclic codes of length 3ps over F-pm have been considered. In this paper, we obtain that the Hamming distances of the repeated root lambda-constacyclic codes of length lps can be determined by the Hamming distances of the simple-root gamma-constacyclic codes of length l, where l is a positive integer and lambda = gamma(ps). Based on this result, the Hamming distances of the repeated root lambda-constacyclic codes of length 3p(s) are given when the generator polynomials have three different irreducible factors. Hence, the Hamming distances of all such constacyclic codes are determined. As an application, we obtain all optimal lambda-constacyclic codes of length 3p(s) with respect to the Griesmer bound and the Singleton bound. Among others, several examples show that some of our codes have the best known parameters with respect to the code tables in [19]. (C) 2020 Elsevier Inc. All rights reserved.
引用
收藏
页数:22
相关论文
共 31 条
[1]   Matrix-product codes over Fq [J].
Blackmore, T ;
Norton, GH .
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2001, 12 (06) :477-500
[2]   On matrix-product structure of repeated-root constacyclic codes over finite fields [J].
Cao, Yonglin ;
Cao, Yuan ;
Dinh, Hai Q. ;
Fu, Fang-Wei ;
Maneejuk, Paravee .
DISCRETE MATHEMATICS, 2020, 343 (04)
[3]   Codes for Symbol-Pair Read Channels [J].
Cassuto, Yuval ;
Blaum, Mario .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2011, 57 (12) :8011-8020
[4]   Codes for Symbol-Pair Read Channels [J].
Cassuto, Yuval ;
Blaum, Mario .
2010 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, 2010, :988-992
[5]   ON REPEATED-ROOT CYCLIC CODES [J].
CASTAGNOLI, G ;
MASSEY, JL ;
SCHOELLER, PA ;
VONSEEMANN, N .
IEEE TRANSACTIONS ON INFORMATION THEORY, 1991, 37 (02) :337-342
[6]   Repeated-root constacyclic codes of length 2lmpn [J].
Chen, Bocong ;
Dinh, Hai Q. ;
Liu, Hongwei .
FINITE FIELDS AND THEIR APPLICATIONS, 2015, 33 :137-159
[7]   Repeated-root constacyclic codes of length lps and their duals [J].
Chen, Bocong ;
Dinh, Hai Q. ;
Liu, Hongwei .
DISCRETE APPLIED MATHEMATICS, 2014, 177 :60-70
[8]   On the linear ordering of some classes of negacyclic and cyclic codes and their distance distributions [J].
Dinh, Hai Q. .
FINITE FIELDS AND THEIR APPLICATIONS, 2008, 14 (01) :22-40
[9]   On the Hamming Distances of Constacyclic Codes of Length 5ps [J].
Dinh, Hai Q. ;
Wang, Xiaoqiang ;
Sirisrisakulchai, Jirakom .
IEEE ACCESS, 2020, 8 :46242-46254
[10]   On the Hamming Distance of Repeated-Root Cyclic Codes of Length 6ps [J].
Dinh, Hai Q. ;
Wang, Xiaoqiang ;
Maneejuk, Paravee .
IEEE ACCESS, 2020, 8 (08) :39946-39958