arXiv subjects
Publications and source records attributed to Fatmanur Gursoy.
In this paper, we solve the reversibility problem for DNA codes over the non-chain ring $R_{k,s}=\mathbb{F}_{4^{2k}}[u_1,...,u_{s}]/< u_1^2-u_1,..., u_s^2-u_s>$. We define an automorphism $θ$ over $R_{k,s}$ which help us both find the idempotent decomposition of $R_{k,s}$ and solve the reversibility problem via skew cyclic codes. Moreover, we introduce a generalized Gray map that preserves DNA reversibility.
Z2Z4-additive codes have been defined as a subgroup of Z2^{r} x Z4^{s} in [5] where Z2, Z4 are the rings of integers modulo 2 and 4 respectively and r and s positive integers. In this study, we define a new family of codes over the set Z2^{r}[\barξ] x Z4^{s}[ξ] where ξis the root of a monic basic primitive polynomial in Z4[x]. We give the standard form of the generator and parity-check matrices of codes over Z2^{r}[\barξ] x Z4^{s}[ξ] and also we introduce skew cyclic codes and their spanning sets over this set.
In this paper we study Z2Z4Z8-additive codes, which are the extension of recently introduced Z2Z4-additive codes. We determine the standard forms of the generator and parity-check matrices of Z2Z4Z8-additive codes. Moreover, we investigate Z2Z4Z8-cyclic codes giving their generator polynomials and spanning sets. We also give some illustrative examples of both Z2Z4Z8-additive codes and Z2Z4Z8-cyclic codes.
In this study we determine the structure of reversible DNA codes obtained from skew cyclic codes. We show that the generators of such DNA codes enjoy some special properties. We study the structural properties of such family of codes and we also illustrate our results with examples.