空军工程大学学报（自然科学版）2013，Vol.14Issue(2)：86-89,4.DOI:10.3969/j.issn.1009-3516.2013.02.019
BCH码的定义集分解及应用
Decomposition of Defining Sets of BCH Codes and Its Applications
摘要
Abstract
Based on basic theory of cyclotomic coset, the concepts of decomposition of defining sets for binary and quaternary BCH codes are introduced respectively this decomposition of defining sets builds up a bridge among the Euclidean orthogonal decomposition of binary BCH codes and Hermitian orthogonal decomposition of quaternary BCH codes. Then the orthogonal decomposition of the dual codes of binary and quaternary BCH codes is also presented. Furtherly, the decomposition of the defining sets of primitive binary and quaternary BCH codes with given designed distances is well studied and solved. Applying the results, some entanglement-assisted quantum codes with good parameters are constructed. The method proposed in this paper devised a new scheme in determining the optimal number of entangled bits, which can simplify the theoretical derivation in constructing entanglement-assisted quantum error correcting codes from classical BCH codes, and also be useful for studying general constructions of entanglement-assisted quantum error correcting codes from cyclic codes.关键词
分圆陪集/BCH码/定义集/纠缠辅助/量子纠错码Key words
cyclotomic coset/ BCH codes/ defining set/ entanglement-assisted/ quantum error correcting codes分类
数理科学引用本文复制引用
李瑞虎,许根,吕良东..BCH码的定义集分解及应用[J].空军工程大学学报（自然科学版）,2013,14(2):86-89,4.基金项目
国家自然科学基金资助项目(11071255) （11071255）
