Constructing DNA Codes using Double Cyclic Codes of Odd and Even Lengths over 픽2 + u픽2.

In this paper, we investigate the algebraic structure and theorems for constructing DNA codes of double cyclic codes of length (α, β) over the finite commutative chain ring 픽₂+u픽₂ with u₂ = 0, where α and β are odd and even positive integers, respectively. Our main objectives include studying the structural properties of these codes, determining their generator polynomials and generating DNA codes from these codes. We investigate theorems for two types of double cyclic codes of length (α, β) over 픽₂ + u픽₂, ideal for generating DNA codes. These codes utilise non-separable structures and satisfy reverse and reverse-complement constraints. Additionally, we propose DNA codes derived from our results. [ABSTRACT FROM AUTHOR]