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Cyclic codes over non-chain ring R(α1, α2, ... , αs) and their applications to quantum and DNA codes

Let s >= 1 be a fixed integer. In this paper, we focus on generating cyclic codes over the ring R(alpha(1), alpha(2), ... , alpha(s)), where alpha(i) is an element of F-q\textbackslash{0}, 1 <= i <= s, by using the Gray map that is defined by the idempotents. Moreover, we describe the proce...

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Main Authors: Ali, Shakir, Alali, Amal S., Wong, Kok Bin, Oztas, Elif Segah, Sharma, Pushpendra
Format: Article
Published: AIMS Press 2024
Subjects:
QA Mathematics
Online Access:http://eprints.um.edu.my/45838/
https://doi.org/10.3934/math.2024358
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spelling my.um.eprints.458382024-11-13T02:43:21Z http://eprints.um.edu.my/45838/ Cyclic codes over non-chain ring R(α1, α2, ... , αs) and their applications to quantum and DNA codes Ali, Shakir Alali, Amal S. Wong, Kok Bin Oztas, Elif Segah Sharma, Pushpendra QA Mathematics Let s >= 1 be a fixed integer. In this paper, we focus on generating cyclic codes over the ring R(alpha(1), alpha(2), ... , alpha(s)), where alpha(i) is an element of F-q\textbackslash{0}, 1 <= i <= s, by using the Gray map that is defined by the idempotents. Moreover, we describe the process to generate an idempotent by using the formula (2.1). As applications, we obtain both optimal and new quantum codes. Additionally, we solve the DNA reversibility problem by introducing F-q reversibility. The aim to introduce the F-q reversibility is to describe IUPAC nucleotide codes, and consequently, 5 IUPAC DNA bases are considered instead of 4 DNA bases (A, T, G, C). AIMS Press 2024 Article PeerReviewed Ali, Shakir and Alali, Amal S. and Wong, Kok Bin and Oztas, Elif Segah and Sharma, Pushpendra (2024) Cyclic codes over non-chain ring R(α1, α2, ... , αs) and their applications to quantum and DNA codes. AIMS Mathematics, 9 (3). pp. 7396-7413. ISSN 2473-6988, DOI https://doi.org/10.3934/math.2024358 <https://doi.org/10.3934/math.2024358>. https://doi.org/10.3934/math.2024358 10.3934/math.2024358
institution Universiti Malaya
building UM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaya
content_source UM Research Repository
url_provider http://eprints.um.edu.my/
topic QA Mathematics
spellingShingle QA Mathematics
Ali, Shakir
Alali, Amal S.
Wong, Kok Bin
Oztas, Elif Segah
Sharma, Pushpendra
Cyclic codes over non-chain ring R(α1, α2, ... , αs) and their applications to quantum and DNA codes
description Let s >= 1 be a fixed integer. In this paper, we focus on generating cyclic codes over the ring R(alpha(1), alpha(2), ... , alpha(s)), where alpha(i) is an element of F-q\textbackslash{0}, 1 <= i <= s, by using the Gray map that is defined by the idempotents. Moreover, we describe the process to generate an idempotent by using the formula (2.1). As applications, we obtain both optimal and new quantum codes. Additionally, we solve the DNA reversibility problem by introducing F-q reversibility. The aim to introduce the F-q reversibility is to describe IUPAC nucleotide codes, and consequently, 5 IUPAC DNA bases are considered instead of 4 DNA bases (A, T, G, C).
format Article
author Ali, Shakir
Alali, Amal S.
Wong, Kok Bin
Oztas, Elif Segah
Sharma, Pushpendra
author_facet Ali, Shakir
Alali, Amal S.
Wong, Kok Bin
Oztas, Elif Segah
Sharma, Pushpendra
author_sort Ali, Shakir
title Cyclic codes over non-chain ring R(α1, α2, ... , αs) and their applications to quantum and DNA codes
title_short Cyclic codes over non-chain ring R(α1, α2, ... , αs) and their applications to quantum and DNA codes
title_full Cyclic codes over non-chain ring R(α1, α2, ... , αs) and their applications to quantum and DNA codes
title_fullStr Cyclic codes over non-chain ring R(α1, α2, ... , αs) and their applications to quantum and DNA codes
title_full_unstemmed Cyclic codes over non-chain ring R(α1, α2, ... , αs) and their applications to quantum and DNA codes
title_sort cyclic codes over non-chain ring r(α1, α2, ... , αs) and their applications to quantum and dna codes
publisher AIMS Press
publishDate 2024
url http://eprints.um.edu.my/45838/
https://doi.org/10.3934/math.2024358
_version_ 1816130465888731136
score 13.214268

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