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- 저자 : Fatmanur Gursoy (검색결과 2 건)
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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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