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Glift codes over chain ring and non-chain ring $R_{e,s}$
Elif Segah Oztas 대한수학회 2022 대한수학회보 Vol.59 No.6
In this paper, Glift codes, generalized lifted polynomials, matrices are introduced. The advantage of Glift code is ``distance preserving" over the ring $\mathcal{R}$. Then optimal codes can be obtained over the rings by using Glift codes and lifted polynomials. Zero divisors are classified to satisfy ``distance preserving" for codes over non-chain rings. Moreover, Glift codes apply on MDS codes and MDS codes are obtained over the ring $\mathcal{R}$ and the non-chain ring $\mathcal{R}_{e,s}$.
$m$-adic residue codes over $F_q \lbrack v \rbrack / (v^2-v)$ and DNA codes
Ferhat Kuruz,Elif Segah Oztas,Irfan Siap 대한수학회 2018 대한수학회보 Vol.55 No.3
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 $F_{4^{2k}}[v]/(v^2-v)$.
m-ADIC RESIDUE CODES OVER F<sub>q</sub>[v]/(v<sup>2</sup> - v) AND DNA CODES
Kuruz, Ferhat,Oztas, Elif Segah,Siap, Irfan Korean Mathematical Society 2018 대한수학회보 Vol.55 No.3
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 $F_{4^{2k}}[v]/(v^2-v)$.