On Linear Codes over Finite Singleton Local Rings-Reference-Cited by-同舟云学术

On Linear Codes over Finite Singleton Local Rings

Published:2024-04-06 Issue:7 Volume:12 Page:1099
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Alabiad Sami¹^ORCID,Alhomaidhi Alhanouf Ali¹^ORCID,Alsarori Nawal A.²^ORCID

Affiliation:

1. Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

2. Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad 431004, India

Abstract

The study of linear codes over local rings, particularly non-chain rings, imposes difficulties that differ from those encountered in codes over chain rings, and this stems from the fact that local non-chain rings are not principal ideal rings. In this paper, we present and successfully establish a new approach for linear codes of any finite length over local rings that are not necessarily chains. The main focus of this study is to produce generating characters, MacWilliams identities and generator matrices for codes over singleton local Frobenius rings of order 32. To do so, we first start by characterizing all singleton local rings of order 32 up to isomorphism. These rings happen to have strong connections to linear binary codes and Z4 codes, which play a significant role in coding theory.

Funder

King Saud University, Riyadh, Saudi Arabia

Publisher

MDPI AG

Link

https://www.mdpi.com/2227-7390/12/7/1099/pdf

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