On DNA codes from a family of chain rings

Year 2017, Volume: 4 Issue: 1, 93 - 102, 11.01.2017

Elif Segah Oztas , Bahattin Yildiz Irfan Siap

https://doi.org/10.13069/jacodesmath.96056

Cited By: 1

Abstract

In this work, we focus on reversible cyclic codes which correspond to
reversible DNA codes or reversible-complement DNA codes over a family of finite chain rings, in an effort to extend what was done by Yildiz and Siap in
\cite{YildizSiap}. The ring family that we have considered are of size $2^{2^k}$, $k=1,2, \cdots$ and we match each ring element with a DNA $2^{k-1}$-mer. We use the so-called $u^2$-adic digit system to solve the reversibility problem and we characterize cyclic codes that correspond to reversible-complement DNA-codes. We then conclude our study with some examples.

Keywords

Cyclic codes, Chain rings, Reversible codes, DNA codes

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