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Let <italic>q</italic> be a power of prime <italic>p</italic>. In this article, we investigate the reversible cyclic codes of arbitrary length <italic>n</italic> over the ring <italic>R</italic> = 𝔽<italic>q</italic> +<italic>u</italic>𝔽<italic>q</italic> + <italic>u</italic>2𝔽<italic>q</italic>, where <italic>u</italic>3 = 0 mod <italic>q</italic>. Further, we find a unique set of generators for cyclic codes over <italic>R</italic> and classify the reversible cyclic codes with their generators. Moreover, it is shown that the dual of reversible cyclic code over <italic>R</italic> is reversible. Finally, some examples of reversible cyclic codes are provided to justify the importance of these results.
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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.

Construction of reversible cyclic codes over 𝔽<italic>q</italic> + <italic>u</italic>𝔽<italic>q</italic> + <italic>u</italic>2𝔽<italic>q</italic>

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Construction of reversible cyclic codes over 𝔽 + 𝔽 + 𝔽

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 =...

Construction of reversible cyclic codes over 𝔽_q + u𝔽_q + u²𝔽_q

Published Online: Mar 27, 2023

Page range: 155 - 176

Received: Sep 20, 2022

Accepted: Dec 22, 2022

DOI: https://doi.org/10.2478/auom-2023-0025

Keywords
Cyclic codes, Codes over rings, Hamming distance, Generator Polynomial

© 2023 Nadeem ur Rehman et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Construction of reversible cyclic codes over 𝔽q + u𝔽q + u2𝔽q

Published Online: Mar 27, 2023

Page range: 155 - 176

Received: Sep 20, 2022

Accepted: Dec 22, 2022

DOI: https://doi.org/10.2478/auom-2023-0025

KeywordsCyclic codes, Codes over rings, Hamming distance, Generator Polynomial

© 2023 Nadeem ur Rehman et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Construction of reversible cyclic codes over 𝔽_q + u𝔽_q + u²𝔽_q

Keywords
Cyclic codes, Codes over rings, Hamming distance, Generator Polynomial