Reversible cyclic codes over a class of chain rings and their application to DNA codes (Q2098085)

Summary: Let \(\mathbb{F}_q\) be a finite field of \(q\) elements and \(R_k = \mathbb{F}_q + u \mathbb{F}_q + \dots + u^{k-1} \mathbb{F}_q\), where \(u^k = 0\), \(k \geq 2\). 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 \(\gcd (n, q) \neq 1\), 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.