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Erschienen in:
18.12.2019
On the Skew Cyclic Codes and the Reversibility Problem for DNA 4-Bases
Erschienen in: Mathematics in Computer Science | Ausgabe 2/2020
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Abstract
The DNA 4-bases are matched with the 256 elements of the finite ring \(R=F_{4}+uF_{4}+vF_{4}+uvF_{4}\), where \( u^{2}=u,v^{2}=v,uv=vu\). By defining a non trivial automorphism over R, the skew cyclic codes over the finite ring R are introduced. The reversible DNA codes are obtained, by using the skew cyclic codes whose generator polynomials satisfy some conditions. Thanks to this, the reversibility problem for DNA 4-bases can be solved. Moreover, the Gray images of the skew cyclic codes over the finite ring are determined.