On cyclic DNA codes over the rings Z4 + wZ4 and Z4 + wZ4 + vZ4 + wvZ4

Abdullah Dertli, Yasemin Cengellenmis

Abstract


The structures of cyclic DNA codes of odd length over the finite rings R = Z4 + wZ4, w^2 = 2 and S = Z4 + wZ4 + vZ4 + wvZ4; w^2 = 2; v^2 =v; wv = vw are studied. The links between the elements of the rings R, S and 16 and 256 codons are established, respectively. The cyclic codes of odd length over the finite ring R satisfy reverse complement constraint and the cyclic codes of odd length over the finite ring S satisfy reverse constraint and reverse complement constraint are studied. The binary images of the cyclic DNA codes over the finite rings R and S are determined. Moreover, a family of DNA skew cyclic codes over R is constructed, its property of being reverse complement is studied.


Keywords


DNA codes; cyclic codes; skew cyclic codes.

Full Text:

PDF


DOI: http://dx.doi.org/10.11145/j.biomath.2017.12.167

BIOMATH is indexed in Mathematical Reviews (MathSciNet), Zentralblatt fuer Mathemathik (zbMATH), EBSCO databasis Academic (Complete, Alite, Premier, Ultimate), Directory of Open Access Journals (DOAJ).

 ISSN: 1314-684X (print), 1314-7218 (online)