A novel approach for constructing reversible codes and applications to DNA codes over the ring F2[u]/(u<

Abstract

A novel approach for constructing reversible codes and applications to DNA codes over the ringIn this work we introduce a novel approach to find reversible codes over different alphabets, using so-called coterm polynomials and a module-construction. We obtain many optimal reversible codes with these constructions. In an attempt to apply the constructions to the DNA, we identify k-bases of DNA with elements in the ring R 2k = F 2 [u]/(u 2k − 1), and by using a form of coterm polynomials, we are able to solve the reversibility and complement problems in DNA codes over this ring. With a freedom on the choice of k we are able to embed any DNA code in a suitable ring, giving an algebraic structure to the DNA codes. We are also able to find reversible and reversible-complement codes that are not necessarily linear cyclic codes.

Reversible DNA codes from skew cyclic codes over a ring of order 256

“…One of the challenging problems in the field is the reversibility problem [18]. This problem arises from the fact that the pairing of nucleotides in two different strands of a DNA sequence is done in opposite direction and reverse order.…”