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Journal of Discrete Mathematical Sciences and Cryptography cover

Journal of Discrete Mathematical Sciences and Cryptography

(Since 1998)
Hybrid ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

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Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

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Journal of Discrete Mathematical Sciences and Cryptography
Open Access Research Article

Algebraic structure of cyclic codes over M3(Fp)

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pp. 189–201Vol. 27Issue 1January 2024DOI: 10.47974/JDMSC-1730 Crossmark XML
Received:
14 Sep 2022
Published Online:
24 Jan 2024
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-1730
Pages:
189–201

Abstract

Let Fp  be the finite field of order p and M3(Fp)  the ring of 3 × 3  matrices over Fp,  where p  is a prime. For certain prime p, we determine the complete algebraic properties of cyclic codes of length N (p | N) over M3(Fp).  We define an isometry from M3(Fp)  to Fp3 + eFp3 + e2Fp3,  where  e3 = 1. As an outcome, we derive numerous optimal and good linear F8  codes induced from F8 -images of cyclic codes over M3(F2).  

Keywords

Matrix ringLinear codeCyclic codeGray mapOptimal code

Subject Classifications

(2010) 94B0594B1594B3594B60

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