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Bull. Korean Math. Soc. 2018; 55(3): 921-935

Online first article March 8, 2018      Printed May 31, 2018

https://doi.org/10.4134/BKMS.b170386

Copyright © The Korean Mathematical Society.

$m$-adic residue codes over $F_q \lbrack v \rbrack / (v^2-v)$ and DNA codes

Ferhat Kuruz, Elif Segah Oztas, Irfan Siap

Yildiz Technical University, Karamanoglu Mehmetbey University, Jacodesmath Institute

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In this study we determine the structure of $m$-adic residue codes over the non-chain ring $F_q[v]/(v^2-v)$ and present some promising examples of such codes that have optimal parameters with respect to Griesmer Bound. Further, we show that the generators of $m$-adic residue codes serve as a natural and suitable application for generating reversible DNA codes via a special automorphism and sets over $F_{4^{2k}}[v]/(v^2-v)$.

Keywords: $m$-adic residue codes, polyadic codes, non-chain rings, cyclic codes, DNA codes

MSC numbers: Primary 94B05, 94B15

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