The structure of duals of cyclic codes over 𝔽2 + u𝔽2 + v𝔽2 + uv𝔽2 and some DNA codes. (2017)

• Record Type: Journal Article
• Authors: Bathala, Srinivasulu; Bhaintwal, Maheshanand
• Is Part Of: International journal of information and coding theory. Volume 4:Number 1(2017)
• Page Start: 79
• Page End: 100
• Publication Date: 2017
• Subjects: DNA codes -- duals -- cyclic codes -- reversible codes -- reversible complement codes; Coding theory -- Periodicals; Information theory -- Periodicals; 003.54
• Languages: English
• ISSNs: 1753-7703

Abstract

In this paper, we study the structure of duals of cyclic codes over the ring R = 𝔽2 + u𝔽2 + v𝔽2 + uv𝔽2, u 2 = v 2 = 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.