Construction of reversible cyclic codes over 𝔽q + u𝔽q + u2𝔽q

Abstract

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 = 𝔽q +u𝔽q + u2𝔽q, 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.

Keywords

• cyclic codes
• codes over rings
• hamming distance
• generator polynomial
• primary 94b15
• secondary 94b05