Title: Reversible cyclic codes over a class of chain rings and their application to DNA codes

Authors: Om Prakash; Shikha Yadav; Priyanka Sharma

Addresses: Department of Mathematics, Indian Institute of Technology Patna, Patna – 801106, India ' Department of Mathematics, Indian Institute of Technology Patna, Patna – 801106, India ' Department of Mathematics, Indian Institute of Technology Patna, Patna – 801106, India

Abstract: Let 𝔽_q be a finite field of q elements and R_k = 𝔽_q + u𝔽_q + … + u^k-1𝔽_q, where u^k = 0, k ≥ 2. This article presents generating set for cyclic codes over R_k and then provides some criteria to check the reversibility of these codes. For positive integers n and q such that gcd(n, q) ≠ 1, there are three presentations for the cyclic codes of length n over R_k. We study all these cases and the case gcd(n, q) = 1 to obtain necessary and sufficient conditions for reversibility. Further, a relation between reversible cyclic codes and reversible-complement cyclic codes is established that plays a crucial role in DNA computing. Finally, we provide some examples to support our study.

Keywords: cyclic codes; generating set; reversible codes; reversible-complement codes; DNA codes.

DOI: 10.1504/IJICOT.2022.125827

International Journal of Information and Coding Theory, 2022 Vol.6 No.1, pp.52 - 70

Received: 10 Dec 2021
Accepted: 11 Jan 2022
Published online: 29 Sep 2022 *

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