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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 $F_{4^{2k}}[v]/(v^2-v)$.
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참고문헌 (15)
참고문헌 신청
T. Abualrub / 2006 / Construction of cyclic codes over GF(4) for DNA computing / J. Franklin Inst. 343(4-5):448~457
L. Adleman / 1994 / Molecular computation of solutions to combinatorial problems / Science 266:1021~1024
A. Bayram / 2016 / Codes over $F_4$ + $vF_4$ and some DNA applications / Des. Codes Cryptogr. 80(2):379~393
R. A. Brualdi / 1989 / Polyadic codes / Discrete Appl. Math. 25(1-2):3~17
X. Dong / 2013 / Generating idempotents of cubic and quartic residue codes over field $F_2$ , Designs, Computer Engineering and Applications / North China Computing Technology Institute 49:41~44
L. Adleman / 1994 / Molecular computation of solutions to combinatorial problems / Science 266:1021~1024
A. Bayram / 2016 / Codes over
R. A. Brualdi / 1989 / Polyadic codes / Discrete Appl. Math. 25(1-2):3~17
X. Dong / 2013 / Generating idempotents of cubic and quartic residue codes over field
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