$m$-adic residue codes over $F_q \lbrack v \rbrack / (v^2-v)$ and DNA codes
Bull. Korean Math. Soc. 2018 Vol. 55, No. 3, 921-935
https://doi.org/10.4134/BKMS.b170386
Published online May 31, 2018
Ferhat Kuruz, Elif Segah Oztas, Irfan Siap
Yildiz Technical University, Karamanoglu Mehmetbey University, Jacodesmath Institute
Abstract : 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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