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The fundamental aim of this research is to analyze the configuration of 𝔽4R submodules, skew cyclic codes over 𝔽4R and establish their connection with DNA codes, where 𝔽4 is a field of order 4 and R = 𝔽4 + u𝔽4 + v𝔽4 + w𝔽4 with u2 = u, v2 = v, w2 = w, uv = vu = 0, vw = wv = 0, wu = uw = 0 is a finite ring. This is achieved by examining particular subclasses like reversible codes. Ultimately, this study aims to utilize Gray maps to derive codes that possess the characteristics of DNA structures. At the end of this paper, we have provided the necessary and sufficient condition for skew cyclic codes to be reversible complement.

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.

The fundamental aim of this research is to analyze the configuration of 픽4R submodules, skew cyclic codes over 픽4R and establish their connection with DNA codes, where 픽4 is a field of order 4 and R = 픽4 + u픽4 + v픽4 + w픽4 with u2 = u, v2 = v, w2 = w, uv = vu = 0, vw = wv = 0, wu = uw = 0 is a finite ring. This is achieved by examining particular subclasses like reversible codes. Ultimately, this study aims to utilize Gray maps to derive codes that possess the characteristics of DNA structures. At the end of this paper, we have provided the necessary and sufficient condition for skew cyclic codes to be reversible complement. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]