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

Abstract

We introduce skew cyclic codes over the finite ring F2 +uF2 +vF2 +wF2 +uvF2 +uwF2 +vwF2 +uvwF2, where u 2 = 0, v 2 = v, w 2 = w, uv = vu, uw = wu, vw = wv and use them to construct reversible DNA codes. The 4-mers are matched with the elements of this ring. The reversibility problem for DNA 4-bases is solved and some examples are provided.

DNA Code from Cyclic and Skew Cyclic Codes over F4[v]/⟨v3⟩

“…Recently, Gursoy et al [18] studied reversible DNA codes by using skew cyclic codes. Later on, Cengellenmis et al [19] studied DNA codes from skew cyclic codes over the rings F 2 [u, v, w], where u 2 = v 2 + v = w 2 + w = uv + vu = uw + wu = vw + wv = 0. Motivated by the above works, we consider cyclic as well as skew cyclic codes over the finite chain ring R = F 4 [v]/ v 3 to construct DNA codes of arbitrary lengths.…”

Cyclic DNA codes over the ring $\mathbb{Z}_4+u\mathbb{Z}_4+u^2\mathbb{Z}_4$

“…In [17] Siap et al studied skew cyclic code of arbitrary length and established a strong connection with well known codes. Most recently, the DNA codes over ring of order 256 has been studied in [9]. They have obtained DNA skew cyclic codes over the ring F 2 + uF 2 + vF 2 + wF 2 + uvF 2 + uwF 2 + vwF 2 + uvwF 2 , where, u 2 = 0, v 2 = v, w 2 = w, uv = vu, uw = wu, vw = wv, addressing reversibility problem.…”