Construction of (σ,δ)-cyclic codes over a non-chain ring and their applications in DNA codes

2023/12/13 by Ashutosh Singh, Priyanka Sharma, Singh, Ashutosh +3
Biochemistry, Genetics and Molecular Biology · Computer Science · #DNA and Biological Computing #Coding theory and cryptography #Advanced biosensing and bioanalysis techniques

paper · pdf · doi:10.48550/arxiv.2312.08109

Abstract

For a prime p and a positive integer m, let \mathbbF_p^m be the finite field of characteristic p, and \mathfrakR_l:=\mathbbF_p^m[v]/⟨ v^l-v⟩ be a non-chain ring. In this paper, we study the (σ,δ)-cyclic codes over \mathfrakR_l. Further, we study the application of these codes in finding DNA codes. Towards this, we first define a Gray map to find classical codes over \mathbbF_p^m using codes over the ring \mathfrakR_l. Later, we find the conditions for a code to be reversible and a DNA code using (σ, δ)-cyclic code. Finally, this algebraic method provides many classical and DNA codes of better parameters.

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