Z4R-additive cyclic and constacyclic codes and MDSS codes

被引：0

作者：

Ghajari, Arazgol ^{[1
]}

Khashyarmanesh, Kazem ^{[1
]}

Abualrub, Taher ^{[2
]}

Siap, Irfan ^{[3
]}

机构：

[1] Ferdowsi Univ Mashhad, Dept Pure Math, POB 1159-91775, Mashhad, Razavi Khorasan, Iran

[2] Amer Univ Sharjah, Dept Math & Stat, Sharjah, U Arab Emirates

[3] Jacodesmath Inst, TR-34220 Istanbul, Turkey

来源：

DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS | 2023年 / 15卷 / 01期

关键词：

Additive cyclic codes; generator polynomials; dual codes and additive constacyclic codes;

D O I：

10.1142/S1793830922500665

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we will study the structure of Z(4)R-additive codes where Z(4) = {0, 1, 2, 3} is the well-known ring of 4 elements and R is the ring given by R = Z(4) + uZ(4) + vZ(4), where u(2) = u, v(2) = v and uv = vu = 0. We will classify all maximum distance separable codes with respect to the Singleton bound (MDSS) over Z(4)R. Then we will focus on Z(4)R-additive cyclic and constacyclic codes. We will find a unique set of generator polynomials for these codes and determine minimum spanning sets for them. We will also find the generator polynomials for the dual of any Z(4)R-additive cyclic or constacyclic code.

引用

页数：21

共 26 条

[21] Z4Z4Z4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb Z_{4}{\mathbb {Z}}_{4}{\mathbb {Z}}_{4}$$\end{document}-additive cyclic codes are asymptotically good [J].

Hai Q. Dinh ;

Bhanu Pratap Yadav ;

Sachin Pathak ;

Abhyendra Prasad ;

Ashish Kumar Upadhyay ;

Woraphon Yamaka .

Applicable Algebra in Engineering, Communication and Computing, 2024, 35 (4) :485-505

[22] On ZprZpsZpt\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}_{p^r} \mathbb {Z}_{p^s} \mathbb {Z}_{p^t}$$\end{document}-additive cyclic codes exhibit asymptotically good properties [J].

Mousumi Ghosh ;

Sachin Pathak ;

Dipendu Maity .

Cryptography and Communications, 2024, 16 (6) :1559-1580

[23] Optimal binary codes derived from F2F4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {F}_{2} \mathbb {F}_4$$\end{document}-additive cyclic codes [J].

Taher Abualrub ;

Nuh Aydin ;

Ismail Aydogdu .

Journal of Applied Mathematics and Computing, 2020, 64 (1-2) :71-87

[24] ℤpℤps\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {Z}_{p}\mathbb {Z}_{p^{s}}$\end{document}-additive cyclic codes are asymptotically good [J].

Ting Yao ;

Shixin Zhu .

Cryptography and Communications, 2020, 12 (2) :253-264

[25] ZpZp[v]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\pmb {{\mathbb {Z}}}}_p{\pmb {{\mathbb {Z}}}}_p[v]$$\end{document}-additive cyclic codes are asymptotically good [J].

Xiaotong Hou ;

Jian Gao .

Journal of Applied Mathematics and Computing, 2021, 66 (1-2) :871-884

[26] On the number of Z2Z4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb {Z}}}_{2}{{\mathbb {Z}}}_{4}$$\end{document} and ZpZp2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb {Z}}}_{p}{{\mathbb {Z}}}_{p^{2}}$$\end{document}-additive cyclic codes [J].

Eda Yildiz ;

Taher Abualrub ;

Ismail Aydogdu .

Applicable Algebra in Engineering, Communication and Computing, 2023, 34 (1) :81-97

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