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Constructions of （q, K, λ, t, Q） almost difference families

Frontiers of Mathematics in China 2014年第2期9卷 377-386页

作者： Lu QIU Dianhua WU Department of Mathematics Guangxi Normal University Guilin 541004 China

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.

关键词： Almost difference family (ADF) cyclotomic class difference family

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The existence of balanced (v, {3,6}, 1) difference families

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Science China(Information Sciences) 2010年第8期53卷 1584-1590页

作者： WU DianHua 1 , CHENG MinQuan 1,2 , CHEN ZhiLin 1 & LUO HaiPeng 3 1 Department of Mathematics, Guangxi Normal University, Guilin 541004, China 2 Institute of Policy and Planning Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan 3 Guangxi Academy of Science, Nanning 530007, China Department of Mathematics Guangxi Normal University Guilin China Institute of Policy and Planning Sciences University of Tsukuba Tsukuba Ibaraki Japan Guangxi Academy of Science Nanning China

Optimal frequency-hopping sequences can be constructed from cyclic (v, K, 1)-PBDs. A (v, K, 1) difference family can be used to construct a (v, K, 1)-PBD. A lot of work has been done on the existence of (v, k, 1) difference families when K = {k} is a singleton. For K = {3, 4}, it is proved that for each prime power v ≡ 1 (mod 18) and v 19, there exists a balanced (v, K, 1) difference family. In this paper, it is proved that there exists a balanced (v, {3, 6}, 1) difference family for each prime power v ≡ 1 (mod 36) and v 37. An infinite class of optimal frequency-hopping sequence is then obtained.

关键词： pairwise balanced design difference family character sum optimal frequency-hopping sequence

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The Existence of (v,4,1) Disjoint difference Families with a Prime Power

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Acta Mathematicae Applicatae Sinica 2008年第4期24卷 643-648页

作者： Dian-hua Wu Jian-xiao Yang Bi-chang Huang Department of Mathematics Guangxi Normal University Guilin 541004 China

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.

关键词： difference family disjoint difference family optimal optical orthogonal codes character sum

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The spectrum of （gv, g, 3, λ）-DF in Zgv

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Science China Mathematics 2009年第5期52卷 1004-1016页

作者： WANG XiaoMiao & CHANG YanXun Institute of Mathematics, Beijing Jiaotong University, Beijing 100044, China Institute of Mathematics Beijing Jiaotong University Beijing China

In this paper, the necessary and sufficient conditions for the existence of a (gv, g, 3, λ)- difference family in Zgv are established. As a consequence, the existence spectrum of a cyclic (3, λ)-GDD of type gv witho... 详细信息

关键词： difference family incomplete difference matrix perfect difference family

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