Construction of reversible cyclic codes over 𝔽_q + u𝔽_q + u²𝔽_q

Let q be a power of prime p. In this article, we investigate the reversible cyclic codes of arbitrary length n over the ring R = 𝔽_q +u𝔽_q + u²𝔽_q, where u³ = 0 mod q. Further, we find a unique set of generators for cyclic codes over R and classify the reversible cyclic codes with their generators. Moreover, it is shown that the dual of reversible cyclic code over R is reversible. Finally, some examples of reversible cyclic codes are provided to justify the importance of these results.