A new set of binary sequences-Periodic Complementary Binary Sequence Pair (PCSP) is proposed. A new class of block design-Difference Family Pair (DFP) is also proposed.The relationship between PCSP and DFP, the proper...A new set of binary sequences-Periodic Complementary Binary Sequence Pair (PCSP) is proposed. A new class of block design-Difference Family Pair (DFP) is also proposed.The relationship between PCSP and DFP, the properties and existing conditions of PCSP and the recursive constructions for PCSP are given.展开更多
Using Galois rings and Galois fields, we construct several infinite classes of partial geometric difference sets, and partial geometric difference families, with new parameters. Furthermore, these partial geometric di...Using Galois rings and Galois fields, we construct several infinite classes of partial geometric difference sets, and partial geometric difference families, with new parameters. Furthermore, these partial geometric difference sets(and partial geometric difference families) correspond to new infinite families of directed strongly regular graphs. We also discuss some of the links between partially balanced designs, 2-adesigns(which were recently coined by Cunsheng Ding in "Codes from Difference Sets"(2015)), and partial geometric designs, and make an investigation into when a 2-adesign is a partial geometric design.展开更多
A （v, k, λ） difference family （（v, k, λ）-DF in short） over an abelian group G of order v, is a collection F=（Bi｜i ∈ I} of k-subsets of G, called base blocks, such that any nonzero element of G can be repres...A （v, k, λ） difference family （（v, k, λ）-DF in short） over an abelian group G of order v, is a collection F=（Bi｜i ∈ I} of k-subsets of G, called base blocks, such that any nonzero element of G can be represented in precisely A ways as a difference of two elements lying in some base blocks in F. A （v, k, λ）-DDF is a difference family with disjoint blocks. In this paper, by using Weil＇s theorem on character sum estimates, it is proved that there exists a （p^n, 4, 1）-DDF, where p = 1 （rood 12） is a prime number and n ≥1.展开更多
The concept of a （q, k, λ, t） almost dltterence tamlly （ADF） nas oeen introduced and studied by C. Ding and J. Yin as a useful generalization of the concept of an almost difference set. In this paper, we consider...The concept of a （q, k, λ, t） almost dltterence tamlly （ADF） nas oeen introduced and studied by C. Ding and J. Yin as a useful generalization of the concept of an almost difference set. In this paper, we consider, more generally, （q, K,λ, t, Q）-ADFs, where K = {k1, k2,.…, kr} is a set of positive integers and Q = （q1,q2,... ,qr） is a given block-size distribution sequence. A necessary condition for the existence of a （q, K, λ, t, Q）-ADF is given, and several infinite classes of （q, K, A, t, Q）-ADFs are constructed.展开更多
Variable-weight optical orthogonal code （OOC） was introduced by G. C. Yang [IEEE Trans. Commun., 1996, 44： 47-55] for multimedia optical CDMA systems with multiple quality of service （QoS） requirements. In this p...Variable-weight optical orthogonal code （OOC） was introduced by G. C. Yang [IEEE Trans. Commun., 1996, 44： 47-55] for multimedia optical CDMA systems with multiple quality of service （QoS） requirements. In this paper, seven new infinite classes of optimal （v, {3,4,6}, 1, Q）-OOCs are constructed.展开更多
Difference systems of sets (DSSs) are combinatorial configurations which were introduced in 1971 by Levenstein for the construction of codes for synchronization. In this paper, we present two kinds of constructions of...Difference systems of sets (DSSs) are combinatorial configurations which were introduced in 1971 by Levenstein for the construction of codes for synchronization. In this paper, we present two kinds of constructions of difference systems of sets by using disjoint difference families and a special type of difference sets, respectively. As a consequence, new infinite classes of optimal DSSs are obtained.展开更多
In an anonymous secret sharing scheme the secret can be reconstructed without knowledge of which participants hold which shares. In this paper some constructions of anonymous secret sharing schemes with 2 thresholds b...In an anonymous secret sharing scheme the secret can be reconstructed without knowledge of which participants hold which shares. In this paper some constructions of anonymous secret sharing schemes with 2 thresholds by using combinatorial designs are given. Let v（t, w, q） denote the minimum size of the set of shares of a perfect anonymous （t, w） threshold secret sharing scheme with q secrets. In this paper we prove that v（t, w, q） - Θ（q） if t and w are fixed and that the lower bound of the size of the set of shares in [4] is not optimal under certain condition.展开更多
In this paper, we give some decompositions of triples of Zp^n or Z3p^n into cyclic triple systems. New constructions of difference families are given. Some infinite classes of simple cyclic triple systems are obtained...In this paper, we give some decompositions of triples of Zp^n or Z3p^n into cyclic triple systems. New constructions of difference families are given. Some infinite classes of simple cyclic triple systems are obtained from these decompositions.展开更多
In this paper, several recursive constructions for directed difference family and perfect directed difference family are presented by means of difference matrix and incomplete difference matrix. Finally the necessary ...In this paper, several recursive constructions for directed difference family and perfect directed difference family are presented by means of difference matrix and incomplete difference matrix. Finally the necessary and sufficient conditions for the existence of a （gv, g, 3, λ）-directed difference family in Zgv are established. As a consequence, the necessary and sufficient conditions for the existence of a cyclic directed group divisible design with block size three and type gv are obtained.展开更多
基金Supported by National Natural Science Foundation of China (69972042),Natural Science Fund of Hebei Provice(599245)and Science Foundation of Yanshan University
文摘A new set of binary sequences-Periodic Complementary Binary Sequence Pair (PCSP) is proposed. A new class of block design-Difference Family Pair (DFP) is also proposed.The relationship between PCSP and DFP, the properties and existing conditions of PCSP and the recursive constructions for PCSP are given.
文摘Using Galois rings and Galois fields, we construct several infinite classes of partial geometric difference sets, and partial geometric difference families, with new parameters. Furthermore, these partial geometric difference sets(and partial geometric difference families) correspond to new infinite families of directed strongly regular graphs. We also discuss some of the links between partially balanced designs, 2-adesigns(which were recently coined by Cunsheng Ding in "Codes from Difference Sets"(2015)), and partial geometric designs, and make an investigation into when a 2-adesign is a partial geometric design.
基金Supported by the National Natural Science Foundation of China(No.10561002)Guangxi Science Foundation(No.0640062)Innovation Project of Guangxi Graduate Education.
文摘A （v, k, λ） difference family （（v, k, λ）-DF in short） over an abelian group G of order v, is a collection F=（Bi｜i ∈ I} of k-subsets of G, called base blocks, such that any nonzero element of G can be represented in precisely A ways as a difference of two elements lying in some base blocks in F. A （v, k, λ）-DDF is a difference family with disjoint blocks. In this paper, by using Weil＇s theorem on character sum estimates, it is proved that there exists a （p^n, 4, 1）-DDF, where p = 1 （rood 12） is a prime number and n ≥1.
基金Acknowledgements The authors wish to thank the anonymous referees for their helpful comments and suggestions that much improved the quality of this paper. The work of Dianhua Wu was supported in part by the National Natural Science Foundation of China （No. 11271089）, the Guangxi Natural Science Foundation （No. 2012GXNSFAA053001）, the Foundation of Guangxi Education Department （No. 201202ZD012）, and the Guangxi ＇Ba Gui＇ Team for Research and Innovation.
文摘The concept of a （q, k, λ, t） almost dltterence tamlly （ADF） nas oeen introduced and studied by C. Ding and J. Yin as a useful generalization of the concept of an almost difference set. In this paper, we consider, more generally, （q, K,λ, t, Q）-ADFs, where K = {k1, k2,.…, kr} is a set of positive integers and Q = （q1,q2,... ,qr） is a given block-size distribution sequence. A necessary condition for the existence of a （q, K, λ, t, Q）-ADF is given, and several infinite classes of （q, K, A, t, Q）-ADFs are constructed.
基金The authors wish to thank the anonymous referees for their comments and suggestions that improved the quality of this paper. This work was supported in part by the National Natural Science Foundation of China （Crant No. 11271089）, Guangxi Science Foundation （Crant No. 2012GXNSFAA053001）, and the Foundation of Cuangxi Education Department （No. 201202ZD012）.
文摘Variable-weight optical orthogonal code （OOC） was introduced by G. C. Yang [IEEE Trans. Commun., 1996, 44： 47-55] for multimedia optical CDMA systems with multiple quality of service （QoS） requirements. In this paper, seven new infinite classes of optimal （v, {3,4,6}, 1, Q）-OOCs are constructed.
基金supported by National Natural Science Foundation of China (Grant Nos.10771051,10831002)
文摘Difference systems of sets (DSSs) are combinatorial configurations which were introduced in 1971 by Levenstein for the construction of codes for synchronization. In this paper, we present two kinds of constructions of difference systems of sets by using disjoint difference families and a special type of difference sets, respectively. As a consequence, new infinite classes of optimal DSSs are obtained.
基金Supported by the National Natural Science Foundation of China(No.10501049,90304012) 973 Project(No.2004CB318000)
文摘In an anonymous secret sharing scheme the secret can be reconstructed without knowledge of which participants hold which shares. In this paper some constructions of anonymous secret sharing schemes with 2 thresholds by using combinatorial designs are given. Let v（t, w, q） denote the minimum size of the set of shares of a perfect anonymous （t, w） threshold secret sharing scheme with q secrets. In this paper we prove that v（t, w, q） - Θ（q） if t and w are fixed and that the lower bound of the size of the set of shares in [4] is not optimal under certain condition.
基金supported by National Natural Science Foundation of China(Grant Nos.11071056 and 10971051)supported by Natural Science and Engineering Research Council of Canada(Grant No.239135-06)
文摘In this paper, we give some decompositions of triples of Zp^n or Z3p^n into cyclic triple systems. New constructions of difference families are given. Some infinite classes of simple cyclic triple systems are obtained from these decompositions.
基金Supported by National Natural Science Foundation of China (Grant No.10771013)
文摘In this paper, several recursive constructions for directed difference family and perfect directed difference family are presented by means of difference matrix and incomplete difference matrix. Finally the necessary and sufficient conditions for the existence of a （gv, g, 3, λ）-directed difference family in Zgv are established. As a consequence, the necessary and sufficient conditions for the existence of a cyclic directed group divisible design with block size three and type gv are obtained.
