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Title: The structure of duals of cyclic codes over 𝔽2 + u𝔽2 + v𝔽2 + uv𝔽2 and some DNA codes

Authors: Srinivasulu Bathala; Maheshanand Bhaintwal

Addresses: Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India ' Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India

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.

Keywords: DNA codes; duals; cyclic codes; reversible codes; reversible complement codes.

DOI: 10.1504/IJICOT.2017.081463

International Journal of Information and Coding Theory, 2017 Vol.4 No.1, pp.79 - 100

Received: 24 Jun 2016
Accepted: 10 Sep 2016

Published online: 02 Jan 2017 *

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