Skew cyclic codes over 𝔻4R and their applications to DNA codes construction

Rehman, Nadeem ur; Ahmad, Mohammad Fareed; Azmi, Mohd

doi:10.2478/auom-2024-0025

Abstract

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.

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Skew cyclic codes over 𝔻4R and their applications to DNA codes construction

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