A novel approach for constructing reversible codes and applications to DNA codes over the ring F-2[u]/(u(2k)-1)

In 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. (C) 2017 Elsevier Inc. All rights reserved.