CHARACTERIZATION OF REVERSIBLE-COMPLEMENT CYCLIC CODES OVER \(\frac{\mathbb{Z}_{4}[w]}{\left\langle w^{2}-2 w\right\rangle}\)

This paper focuses on the characterization of reversible and reversible-complement codes using cyclic codes over \(\mathbb{Z}_{4}[w] /\left\langle w^{2}-2 w\right\rangle\). We provide some necessary and sufficient conditions for a cyclic code of > odd length over \(\mathbb{Z}_{4}[w] /\left\langle w^{2}-2 w\right\rangle\) to be a reversible code. In particular, we derive some restrictions on polynomial generators of cyclic codes to construct reversible codes. By linking the elements of this ring to the DNA double base, we characterize reversible-complement codes and explore DNA codes from cyclic codes.