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arXiv · 2606.06367

Reversible double cyclic codes over a chain ring

Mohd Anwar·Mohd Arif Raza·Mohd Rashid·Muzibur Rahman Mozumder
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Abstract

In this paper, we study the structure of double cyclic codes of length $(γ,δ)$ over $\mathbb F_q+u\mathbb F_q, u^2=0$. We also study the dual of double cyclic code of length $(γ,δ)$ and give a minimal spanning set of double cyclic codes. Moreover, we study the necessary and sufficient conditions for a double cyclic code to be reversible and reversible-complement double cyclic code and with the help of these codes, we constructed DNA codes over $\mathbb F_4+u\mathbb F_4, u^2=0$. We also constructed some optimal codes to support our results.

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Mohd Anwar, Mohd Arif Raza, Mohd Rashid, Muzibur Rahman Mozumder. 2026-06-04. Reversible double cyclic codes over a chain ring. https://arxiv.org/abs/2606.06367

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