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RISS 인기검색어
- 검색키워드
- 저자 : Irfan Siap (검색결과 8 건)
- 무료
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- 유료
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On quantum codes from cyclic codes over a class of nonchain rings
Mustafa Sari,Irfan Siap 대한수학회 2016 대한수학회보 Vol.53 No.6
In this paper, we extend the results given in \cite{2.5} to a nonchain ring $R_p={\mathbb{F}_p} + v{\mathbb{F}_p} + \cdots + {v^{p - 1}}{\mathbb{F}_p}$, where ${v^p} = v$ and $p$ is a prime. We determine the structure of the cyclic codes of arbitrary length over the ring $R_p$ and study the structure of their duals. We classify cyclic codes containing their duals over $R_p$ by giving necessary and sufficient conditions. Further, by taking advantage of the Gray map $\pi$ defined in \cite{2.7}, we give the parameters of the quantum codes of length $pn$ over $\mathbb{F}_p$ which are obtained from cyclic codes over $R_p.$ Finally, we illustrate the results by giving some examples.
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ONE-HOMOGENEOUS WEIGHT CODES OVER FINITE CHAIN RINGS
SARI, MUSTAFA,SIAP, IRFAN,SIAP, VEDAT Korean Mathematical Society 2015 대한수학회보 Vol.52 No.6
This paper determines the structures of one-homogeneous weight codes over finite chain rings and studies the algebraic properties of these codes. We present explicit constructions of one-homogeneous weight codes over finite chain rings. By taking advantage of the distance-preserving Gray map defined in [7] from the finite chain ring to its residue field, we obtain a family of optimal one-Hamming weight codes over the residue field. Further, we propose a generalized method that also includes the examples of optimal codes obtained by Shi et al. in [17].
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ON QUANTUM CODES FROM CYCLIC CODES OVER A CLASS OF NONCHAIN RINGS
Sari, Mustafa,Siap, Irfan Korean Mathematical Society 2016 대한수학회보 Vol.53 No.6
In this paper, we extend the results given in [3] to a nonchain ring $R_p={\mathbb{F}}_p+v{\mathbb{F}}_p+{\cdots}+v^{p-1}{\mathbb{F}}_p$, where $v^p=v$ and p is a prime. We determine the structure of the cyclic codes of arbitrary length over the ring $R_p$ and study the structure of their duals. We classify cyclic codes containing their duals over $R_p$ by giving necessary and sufficient conditions. Further, by taking advantage of the Gray map ${\pi}$ defined in [4], we give the parameters of the quantum codes of length pn over ${\mathbb{F}}_p$ which are obtained from cyclic codes over $R_p$. Finally, we illustrate the results by giving some examples.
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ONE-HOMOGENEOUS WEIGHT CODES OVER FINITE CHAIN RINGS
Mustafa Sari,Irfan Siap,Vedat Siap 대한수학회 2015 대한수학회보 Vol.52 No.6
This paper determines the structures of one-homogeneous weight codes over finite chain rings and studies the algebraic properties of these codes. We present explicit constructions of one-homogeneous weight codes over finite chain rings. By taking advantage of the distance- preserving Gray map defined in [7] from the finite chain ring to its residue field, we obtain a family of optimal one-Hamming weight codes over the residue field. Further, we propose a generalized method that also includes the examples of optimal codes obtained by Shi et al. in [17].
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On generalizations of skew quasi-cyclic codes
Sumeyra Bedir,Fatmanur Gursoy,Irfan Siap 대한수학회 2020 대한수학회보 Vol.57 No.2
In the last two decades, codes over noncommutative rings have been one of the main trends in coding theory. Due to the fact that noncommutativity brings many challenging problems in its nature, still there are many open problems to be addressed. In 2015, generator polynomial matrices and parity-check polynomial matrices of generalized quasi-cyclic (GQC) codes were investigated by Matsui. We extended these results to the noncommutative case. Exploring the dual structures of skew constacyclic codes, we present a direct way of obtaining parity-check polynomials of skew multi-twisted codes in terms of their generators. Further, we lay out the algebraic structures of skew multi-polycyclic codes and their duals and we give some examples to illustrate the theorems.
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ON GENERALIZATIONS OF SKEW QUASI-CYCLIC CODES
Bedir, Sumeyra,Gursoy, Fatmanur,Siap, Irfan Korean Mathematical Society 2020 대한수학회보 Vol.57 No.2
In the last two decades, codes over noncommutative rings have been one of the main trends in coding theory. Due to the fact that noncommutativity brings many challenging problems in its nature, still there are many open problems to be addressed. In 2015, generator polynomial matrices and parity-check polynomial matrices of generalized quasi-cyclic (GQC) codes were investigated by Matsui. We extended these results to the noncommutative case. Exploring the dual structures of skew constacyclic codes, we present a direct way of obtaining parity-check polynomials of skew multi-twisted codes in terms of their generators. Further, we lay out the algebraic structures of skew multipolycyclic codes and their duals and we give some examples to illustrate the theorems.
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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 $F_{4^{2k}}[v]/(v^2-v)$.
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$m$-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 $F_{4^{2k}}[v]/(v^2-v)$.
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