In consideration of decoding cydic codes, a general formula for error pattern prediction is obtained. It extends the Welch-Berlekamp theorem and expands the Welch-Berlekamp algorithm, so that the limitation from BCH b...In consideration of decoding cydic codes, a general formula for error pattern prediction is obtained. It extends the Welch-Berlekamp theorem and expands the Welch-Berlekamp algorithm, so that the limitation from BCH bound is broken, and the algorithm turns into a universal one which meets the actual minimum distance as well as complete decoding beyond the minimum distance in the case of decoding BCH codes and general cydic codes.展开更多
In recent years, there have been intensive activities in the area of constructing quantum maximum distance separable(MDS for short) codes from constacyclic MDS codes through the Hermitian construction. In this paper, ...In recent years, there have been intensive activities in the area of constructing quantum maximum distance separable(MDS for short) codes from constacyclic MDS codes through the Hermitian construction. In this paper, a new class of quantum MDS code is constructed, which extends the result of [Theorems 3.14–3.15, Kai, X., Zhu, S., and Li,P., IEEE Trans. on Inf. Theory, 60(4), 2014, 2080–2086], in the sense that our quantum MDS code has bigger minimum distance.展开更多
基金the National Natural Science Foundation of China, the Military Science Foundation of the Electronic Industrial Ministry of China and Frderung der Wissenschaft Foundation of Austria
文摘In consideration of decoding cydic codes, a general formula for error pattern prediction is obtained. It extends the Welch-Berlekamp theorem and expands the Welch-Berlekamp algorithm, so that the limitation from BCH bound is broken, and the algorithm turns into a universal one which meets the actual minimum distance as well as complete decoding beyond the minimum distance in the case of decoding BCH codes and general cydic codes.
基金supported by the National Natural Science Foundation of China(Nos.11171150,113711138,11531002)the Foundation of Science and the Technology on Information Assurance Laboratory(No.KJ-15-009)
文摘In recent years, there have been intensive activities in the area of constructing quantum maximum distance separable(MDS for short) codes from constacyclic MDS codes through the Hermitian construction. In this paper, a new class of quantum MDS code is constructed, which extends the result of [Theorems 3.14–3.15, Kai, X., Zhu, S., and Li,P., IEEE Trans. on Inf. Theory, 60(4), 2014, 2080–2086], in the sense that our quantum MDS code has bigger minimum distance.
