Construction of reversible cyclic codes over 𝔽q + u𝔽q + u2𝔽q

Nadeem ur Rehman; Mohammad Fareed Ahmad; Mohd Azmi

doi:10.2478/auom-2023-0025

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Construction of reversible cyclic codes over 𝔽q + u𝔽q + u2𝔽q

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 31 (2023): Issue 2 (March 2023)

By: Nadeem ur Rehman, Mohammad Fareed Ahmad and Mohd Azmi

Open Access

|Mar 2023

Abstract

Let q be a power of prime p. In this article, we investigate the reversible cyclic codes of arbitrary length n over the ring R = 𝔽_q +u𝔽_q + u²𝔽_q, where u³ = 0 mod q. Further, we find a unique set of generators for cyclic codes over R and classify the reversible cyclic codes with their generators. Moreover, it is shown that the dual of reversible cyclic code over R is reversible. Finally, some examples of reversible cyclic codes are provided to justify the importance of these results.

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Articles in this issue

DOI: https://doi.org/10.2478/auom-2023-0025 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

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Language: English

Page range: 155 - 176

Submitted on: Sep 20, 2022

Accepted on: Dec 22, 2022

Published on: Mar 27, 2023

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

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© 2023 Nadeem ur Rehman, Mohammad Fareed Ahmad, Mohd Azmi, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 31 (2023): Issue 2 (March 2023)