DNA Code from Cyclic and Skew Cyclic Codes over F4[v]/⟨v3⟩

Abstract

The main motivation of this work is to study and obtain some reversible and DNA codes of length n with better parameters. Here, we first investigate the structure of cyclic and skew cyclic codes over the chain ring R:=F4[v]/⟨v3⟩. We show an association between the codons and the elements of R using a Gray map. Under this Gray map, we study reversible and DNA codes of length n. Finally, several new DNA codes are obtained that have improved parameters than previously known codes. We also determine the Hamming and the Edit distances of these codes.

DNA Images of Codes Over F4t [u]/<uk>

“…In this paper, we focus on DNA images of codes over chain rings S = F 4 t [u]/ u k . This may be considered as a partial answer to the question asked in [20,22] about the generalization of the ring they used. In Section 2, we begin with mapping the elements of S to R = F 4 [v]/ v tk and use R for the formulation of DNA codes for the rest of our work.…”

“…Algebraic construction of codes over fields and rings is an established approach [11,12]. Similarly, composition of DNA codes are studied over the rings F 2 + uF 2 in [13,14], F 2 + uF 2 + vF 2 + uvF 2 in [15], F 2 [u]/(u 2k − 1) in [16], Z 4 [v]/(v 2 − v) in [17], Z 4 [u]/ u 2 − 1 in [18], Z 4 + vZ 4 in [19], F 2 [u]/(u 4 − 1) in [20] and F 4 [u]/ u 3 in [21,22]. Further, DNA codes are studied over skew polynomial rings in [23] and Galois rings in [24].…”

DNA Images of Codes Over F4t [u]/<uk>

“…In this paper, we focus on DNA images of codes over chain rings S = F 4 t [u]/ u k . This may be considered as a partial answer to the question asked in [20,22] about the generalization of the ring R. In Section 2, we begin with mapping the elements of S to R = F 4 [v]⁄ v tk and use R for the formulation of DNA codes for the rest of our work. We relate each element of R to a DNA strand of length 4 tk using the Gray map η and one-to-one correspondence σ to the DNA alphabet S D4 .…”

Mathematical Modeling in Systems Biology

“…The study conducted by Om Prakash et al is related to DNA-based computing, which relies on error control coding techniques [7]. Coding theory is applied to construct a large set of DNA strings that satisfy certain combinatorial constraints.…”