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

Abstract

We introduce skew cyclic codes over the finite ring

$$\mathbb{F}_2+u\mathbb{F}_2+v\mathbb{F}_2+w\mathbb{F}_2+uv\mathbb{F}_2+uw\mathbb{F}_2+vw\mathbb{F}_2+uvw\mathbb{F}_2,$$

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.

Received: 28 December 2019 | Accepted: 24 August 2020