Fraction repetition(FR)codes are integral in distributed storage systems(DSS)with exact repair-by-transfer,while pliable fraction repetition codes are vital for DSSs in which both the per-node storage and repetition d...Fraction repetition(FR)codes are integral in distributed storage systems(DSS)with exact repair-by-transfer,while pliable fraction repetition codes are vital for DSSs in which both the per-node storage and repetition degree can easily be adjusted simultaneously.This paper introduces a new type of pliable FR codes,called absolute balanced pliable FR(ABPFR)codes,in which the access balancing in DSS is considered.Additionally,the equivalence between pliable FR codes and resolvable transversal packings in combinatorial design theory is presented.Then constructions of pliable FR codes and ABPFR codes based on resolvable transversal packings are presented.展开更多
Codebooks are widely applied in code division multiple access communication systems.Based on the subspaces of singular linear spaces over the finite fields,two classes of new codebooks are constructed.Firstly,a kind o...Codebooks are widely applied in code division multiple access communication systems.Based on the subspaces of singular linear spaces over the finite fields,two classes of new codebooks are constructed.Firstly,a kind of binary codebooks are constructed by using the subspace of the singular linear space over the finite fields.According to the anzahl theorem,the parameters and the maximum correlation amplitude I_(max)(C)of the codebooks are calculated,and then given the conditions that the I_(max)(C)asymptotically reaches the Welch bound.On this basis,by mixing with Hadamard matrices,the number of columns are increased and obtain another class of new code,which further relaxes the conditions that the I_(max)(C)asymptotically reaches the Welch bound.展开更多
研究具有几乎单型的区传递自同构群的区传递Steine 5-设计的分类问题。利用二齐次置换群分类定理证明了:一个具有几乎单型区传递自同构群G的Steiner 5-设计D,则要么是一个5-(12,6,1)设计且自同构群G≅M12或者是一个5-(24,8,1)且自同构群G...研究具有几乎单型的区传递自同构群的区传递Steine 5-设计的分类问题。利用二齐次置换群分类定理证明了:一个具有几乎单型区传递自同构群G的Steiner 5-设计D,则要么是一个5-(12,6,1)设计且自同构群G≅M12或者是一个5-(24,8,1)且自同构群G≅M24,要么设计的自同构群G的基柱Socle(G)只能是典型单群。The classification problem of block-transitive Steiner 5-designs with an almost simple block-transitive automorphism group is studied. By using the classification theorem of 2-homogeneous permutation groups, it is proved that if the Steiner 5-design has an almost simple block-transitive automorphism group, then either it is a 5-(12,6,1)design and the automorphism G≅M12or it is a 5-(24,8,1)design and the automorphism G≅M24, or the socle of the automorphism G, Socle(G)can only be a classical simple group.展开更多
基金Supported in part by the National Key R&D Program of China(No.2020YFA0712300)NSFC(No.61872353)。
文摘Fraction repetition(FR)codes are integral in distributed storage systems(DSS)with exact repair-by-transfer,while pliable fraction repetition codes are vital for DSSs in which both the per-node storage and repetition degree can easily be adjusted simultaneously.This paper introduces a new type of pliable FR codes,called absolute balanced pliable FR(ABPFR)codes,in which the access balancing in DSS is considered.Additionally,the equivalence between pliable FR codes and resolvable transversal packings in combinatorial design theory is presented.Then constructions of pliable FR codes and ABPFR codes based on resolvable transversal packings are presented.
文摘Codebooks are widely applied in code division multiple access communication systems.Based on the subspaces of singular linear spaces over the finite fields,two classes of new codebooks are constructed.Firstly,a kind of binary codebooks are constructed by using the subspace of the singular linear space over the finite fields.According to the anzahl theorem,the parameters and the maximum correlation amplitude I_(max)(C)of the codebooks are calculated,and then given the conditions that the I_(max)(C)asymptotically reaches the Welch bound.On this basis,by mixing with Hadamard matrices,the number of columns are increased and obtain another class of new code,which further relaxes the conditions that the I_(max)(C)asymptotically reaches the Welch bound.
文摘研究具有几乎单型的区传递自同构群的区传递Steine 5-设计的分类问题。利用二齐次置换群分类定理证明了:一个具有几乎单型区传递自同构群G的Steiner 5-设计D,则要么是一个5-(12,6,1)设计且自同构群G≅M12或者是一个5-(24,8,1)且自同构群G≅M24,要么设计的自同构群G的基柱Socle(G)只能是典型单群。The classification problem of block-transitive Steiner 5-designs with an almost simple block-transitive automorphism group is studied. By using the classification theorem of 2-homogeneous permutation groups, it is proved that if the Steiner 5-design has an almost simple block-transitive automorphism group, then either it is a 5-(12,6,1)design and the automorphism G≅M12or it is a 5-(24,8,1)design and the automorphism G≅M24, or the socle of the automorphism G, Socle(G)can only be a classical simple group.
