The structure of duals of cyclic codes over 𝔽<SUB align="right">2 + u𝔽<SUB align="right">2 + v𝔽<SUB align="right">2 + uv𝔽<SUB align="right">2 and some DNA codes

Abstract

In this paper, we study the structure of duals of cyclic codes over the ring R = F2 + uF2 + vF2 + uvF2, u2 = v2 = 0, uv = vu. We determine a unique set of generators for these codes. We also determine a minimal spanning set for a class of cyclic codes of odd length over R. A sufficient condition for a cyclic code of odd length over R to contain its dual is presented. We give a necessary and sufficient condition for a cyclic code of odd lengths over R to be reversible complement. Further, we construct DNA codes as images of reversible complement cyclic codes of odd length over R.