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Construction of reversible cyclic codes over 𝔽q + u𝔽q + u2𝔽q Cover
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 = 𝔽q +u𝔽q + u2𝔽q, 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.

DOI: https://doi.org/10.2478/auom-2023-0025 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 155 - 176
Submitted on: Sep 20, 2022
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Accepted on: Dec 22, 2022
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Published on: Mar 27, 2023
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 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.