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Erschienen in: Designs, Codes and Cryptography 2/2016

01.08.2016

Codes over \(F_{4}+vF_4\) and some DNA applications

verfasst von: Aysegul Bayram, Elif Segah Oztas, Irfan Siap

Erschienen in: Designs, Codes and Cryptography | Ausgabe 2/2016

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Abstract

In this work, we study the structure of linear, constacyclic and cyclic codes over the ring \(R=F_{4}[v]/(v^{2}-v)\) and establish relations to codes over \( F_{4}\) by defining a Gray map between R and \(F_{4}^{2}\) where \(F_4\) is the field with 4 elements. Constacyclic codes over R are shown to be principal ideals. Further, we study skew constacyclic codes over R. The structure of all skew constacyclic codes is completely determined. Furthermore, we introduce reversible codes which provide a rich source for DNA codes. We conclude the paper by obtaining some DNA codes over R that attain the Griesmer bound.
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Metadaten
Titel
Codes over and some DNA applications
verfasst von
Aysegul Bayram
Elif Segah Oztas
Irfan Siap
Publikationsdatum
01.08.2016
Verlag
Springer US
Erschienen in
Designs, Codes and Cryptography / Ausgabe 2/2016
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-015-0100-8

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