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Designs, Codes and Cryptography
Published in: Designs, Codes and Cryptography 2/2016

01-08-2016

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

Authors: Aysegul Bayram, Elif Segah Oztas, Irfan Siap

Published in: Designs, Codes and Cryptography | Issue 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.
previous article Squaring attacks on McEliece public-key cryptosystems using quasi-cyclic codes of even dimension
next article Convolutional block codes with cryptographic properties over the semi-direct product
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Metadata
Title
Codes over and some DNA applications
Authors
Aysegul Bayram
Elif Segah Oztas
Irfan Siap
Publication date
01-08-2016
Publisher
Springer US
Published in
Designs, Codes and Cryptography / Issue 2/2016
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-015-0100-8

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