It is a regular way of constructing quantum error-correcting codes via codes with self-orthogonal property, and whether a classical Bose-Chaudhuri-Hocquenghem (BCH) code is self-orthogonal can be determined by its des...It is a regular way of constructing quantum error-correcting codes via codes with self-orthogonal property, and whether a classical Bose-Chaudhuri-Hocquenghem (BCH) code is self-orthogonal can be determined by its designed distance. In this paper, we give the sufficient and necessary condition for arbitrary classical BCH codes with self-orthogonal property through algorithms. We also give a better upper bound of the designed distance of a classical narrow-sense BCH code which contains its Euclidean dual. Besides these, we also give one algorithm to compute the dimension of these codes. The complexity of all algorithms is analyzed. Then the results can be applied to construct a series of quantum BCH codes via the famous CSS constructions.展开更多
Given the potential for bit flipping of data on a memory medium,a high-speed parallel Bose-Chaudhuri-Hocquenghem(BCH)error correction scheme with modular characteristics,combining logic implementation and a look-up ta...Given the potential for bit flipping of data on a memory medium,a high-speed parallel Bose-Chaudhuri-Hocquenghem(BCH)error correction scheme with modular characteristics,combining logic implementation and a look-up table,is proposed.It is suitable for data error correction on a modern field programmable gate array full with on-chip embedded memories.We elaborate on the optimization method for each part of the system and analyze the realization process of this scheme in the case of the BCH code with an information bit length of 1024 bits and a code length of 1068 bits that corrects the 4-bit error.展开更多
基金Supported by the National Natural Science Foundation of China (No.60403004)the Outstanding Youth Foundation of China (No.0612000500)
文摘It is a regular way of constructing quantum error-correcting codes via codes with self-orthogonal property, and whether a classical Bose-Chaudhuri-Hocquenghem (BCH) code is self-orthogonal can be determined by its designed distance. In this paper, we give the sufficient and necessary condition for arbitrary classical BCH codes with self-orthogonal property through algorithms. We also give a better upper bound of the designed distance of a classical narrow-sense BCH code which contains its Euclidean dual. Besides these, we also give one algorithm to compute the dimension of these codes. The complexity of all algorithms is analyzed. Then the results can be applied to construct a series of quantum BCH codes via the famous CSS constructions.
基金Project supported by the National Natural Science Foundation of China(No.61973280)the China Postdoctoral Science Foundation(No.2019M661069)。
文摘Given the potential for bit flipping of data on a memory medium,a high-speed parallel Bose-Chaudhuri-Hocquenghem(BCH)error correction scheme with modular characteristics,combining logic implementation and a look-up table,is proposed.It is suitable for data error correction on a modern field programmable gate array full with on-chip embedded memories.We elaborate on the optimization method for each part of the system and analyze the realization process of this scheme in the case of the BCH code with an information bit length of 1024 bits and a code length of 1068 bits that corrects the 4-bit error.
