Reversible double cyclic codes over a chain ring
In this paper, we study the structure of double cyclic codes of length $(\gamma,\delta)$ over $\mathbb F_q+u\mathbb F_q, u^2=0$. We also study the dual of double cyclic code of length $(\gamma,\delta)$ 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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