Reversible DNA codes over a family of non-chain rings

In this work we extend results introduced in [15]. Especially, we solve the reversibility problem for DNA codes over the non chain ring $R_{k,s}=F_{4^{2k}}[u_1,\ldots,u_{s}]/\langle u_1^2-u_1,\ldots, u_s^2-u_s\rangle$. We define an automorphism $\theta$ over $R_{k,s}$ which helps us both finding the idempotent decomposition of $R_{k,s}$ and solving the reversibility problem via skew cyclic codes. Moreover, we introduce a generalized Gray map that preserves DNA reversibility.Comment: 10 page

Reversible Codes and Its Application to Reversible DNA Codes over F4kF_{4^k}

Coterm polynomials are introduced by Oztas et al. [a novel approach for constructing reversible codes and applications to DNA codes over the ring $F_2[u]/(u^{2k}-1)$, Finite Fields and Their Applications 46 (2017).pp. 217-234.], which generate reversible codes. In this paper, we generalize the coterm polynomials and construct some reversible codes which are optimal codes by using $m$-quasi-reciprocal polynomials. Moreover, we give a map from DNA $k$-bases to the elements of $F_{4^k}$, and construct reversible DNA codes over $F_{4^k}$ by DNA-$m$-quasi-reciprocal polynomials

Cyclic DNA codes over F2+uF2+vF2+uvF2

In this work, we study the structure of cyclic DNA codes of arbitrary lengths over the ring R=F2+uF2+vF2+uvF2 and establish relations to codes over R1=F2+uF2 by defining a Gray map between R and R1^2 where R1 is the ring with 4 elements. Cyclic codes of arbitrary lengths over R satisfied the reverse constraint and the reverse-complement constraint are studied in this paper. The GC content constraint is considered in the last

The Art of DNA Strings: Sixteen Years of DNA Coding Theory

The idea of computing with DNA was given by Tom Head in 1987, however in 1994 in a seminal paper, the actual successful experiment for DNA computing was performed by Adleman. The heart of the DNA computing is the DNA hybridization, however, it is also the source of errors. Thus the success of the DNA computing depends on the error control techniques. The classical coding theory techniques have provided foundation for the current information and communication technology (ICT). Thus it is natural to expect that coding theory will be the foundational subject for the DNA computing paradigm. For the successful experiments with DNA computing usually we design DNA strings which are sufficiently dissimilar. This leads to the construction of a large set of DNA strings which satisfy certain combinatorial and thermodynamic constraints. Over the last 16 years, many approaches such as combinatorial, algebraic, computational have been used to construct such DNA strings. In this work, we survey this interesting area of DNA coding theory by providing key ideas of the area and current known results.Comment: 19 pages, 4 figures, draft review on DNA code