This paper discusses optimal binary codes and pure binary quantum codes created using Steane construction. First, a local search algorithm for a special subclass of quasi-cyclic codes is proposed, then five binary qua...This paper discusses optimal binary codes and pure binary quantum codes created using Steane construction. First, a local search algorithm for a special subclass of quasi-cyclic codes is proposed, then five binary quasi-cyclic codes are built. Second, three classical construction methods are generalized for new codes from old such that they are suitable for constructing binary self-orthogonal codes, and 62 binary codes and six subcode chains of obtained self-orthogonal codes are designed. Third, six pure binary quantum codes are constructed from the code pairs obtained through Steane construction. There are 66 good binary codes that include 12 optimal linear codes, 45 known optimal linear codes, and nine known optimal self-orthogonal codes. The six pure binary quantum codes all achieve the performance of their additive counterparts constructed by quaternary construction and thus are known optimal codes.展开更多
A new description of the additive quantum codes is presented and a new way to construct good quantum codes [[n, k, d]] is given by using classical binary codes with specific properties in F2^3n. We show several conseq...A new description of the additive quantum codes is presented and a new way to construct good quantum codes [[n, k, d]] is given by using classical binary codes with specific properties in F2^3n. We show several consequences and examples of good quantum codes by using our new description of the additive quantum codes.展开更多
The weight hierarchy of a binary linear [n, k] code C is the sequence (d 1, d 2, . . . , d k ), where d r is the smallest support of an r-dimensional subcode of C. The codes of dimension 4 are collected in classes and...The weight hierarchy of a binary linear [n, k] code C is the sequence (d 1, d 2, . . . , d k ), where d r is the smallest support of an r-dimensional subcode of C. The codes of dimension 4 are collected in classes and the possible weight hierarchies in each class is determined by finite projective geometries. The possible weight hierarchies in class A, B, C, D are determined in Part (I). The possible weight hierarchies in class E, F, G, H, I are determined in Part (II).展开更多
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant No. 11071255） and Science Foundation for young teachers in Science College, Air Force Engineering University. The authors are very grateful to the anonymous referees and the editors for their valuable comments and suggestions, which help to improve the manuscript significantly.
文摘This paper discusses optimal binary codes and pure binary quantum codes created using Steane construction. First, a local search algorithm for a special subclass of quasi-cyclic codes is proposed, then five binary quasi-cyclic codes are built. Second, three classical construction methods are generalized for new codes from old such that they are suitable for constructing binary self-orthogonal codes, and 62 binary codes and six subcode chains of obtained self-orthogonal codes are designed. Third, six pure binary quantum codes are constructed from the code pairs obtained through Steane construction. There are 66 good binary codes that include 12 optimal linear codes, 45 known optimal linear codes, and nine known optimal self-orthogonal codes. The six pure binary quantum codes all achieve the performance of their additive counterparts constructed by quaternary construction and thus are known optimal codes.
基金The work was supported in part by Harbin Normal University's Natural Scientific fund items (KM2006-20 and KM2005-14)Educational department scientific Technology item (1151112)Postdoctorate's fund item (LRB-KY01043)Scientific Technology Brainstorm item in Hei Longjiang province
文摘A new description of the additive quantum codes is presented and a new way to construct good quantum codes [[n, k, d]] is given by using classical binary codes with specific properties in F2^3n. We show several consequences and examples of good quantum codes by using our new description of the additive quantum codes.
基金supported by The Norwegian Research Councilthe National Science Foundation of China(10271116)
文摘The weight hierarchy of a binary linear [n, k] code C is the sequence (d 1, d 2, . . . , d k ), where d r is the smallest support of an r-dimensional subcode of C. The codes of dimension 4 are collected in classes and the possible weight hierarchies in each class is determined by finite projective geometries. The possible weight hierarchies in class A, B, C, D are determined in Part (I). The possible weight hierarchies in class E, F, G, H, I are determined in Part (II).
基金supported by National Natural Science Foundation of China(61401525,61471133)University Outstanding Young Teacher Training Program of Guangdong Province(YQ2015092)+1 种基金Province Science and Technology Project of Guangdong Province(2017A070712019,2016a040402043)Higher Education High Level Talent Fund of Guangdong Province(2016KZDXM001)
