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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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참고문헌 (35)
참고문헌 신청
Taher Abualrub / 2010 / On the Construction of Skew Quasi-Cyclic Codes / IEEE Transactions on Information Theory 56(5):2081~2090
Adel Alahmadi / 2016 / On the duality and the direction of polycyclic codes / Advances in Mathematics of Communications 10(4):921~929
Nuh Aydin / 2017 / A generalization of quasi-twisted codes: Multi-twisted codes / Finite Fields and Their Applications 45:96~106
N. Aydin / 2001 / The structure of 1-generator quasi-twisted codes and new linear codes / Des. Codes Cryptogr 23(3):313~326
S. Bedir / 2015 / Polycyclic codes over finite chain rings / International Conference on Coding and Cryptography
Adel Alahmadi / 2016 / On the duality and the direction of polycyclic codes / Advances in Mathematics of Communications 10(4):921~929
Nuh Aydin / 2017 / A generalization of quasi-twisted codes: Multi-twisted codes / Finite Fields and Their Applications 45:96~106
N. Aydin / 2001 / The structure of 1-generator quasi-twisted codes and new linear codes / Des. Codes Cryptogr 23(3):313~326
S. Bedir / 2015 / Polycyclic codes over finite chain rings / International Conference on Coding and Cryptography
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