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

作　　者：Dian-hua Wu Jian-xiao Yang Bi-chang Huang 

机构地区：[1]Department of Mathematics, Guangxi Normal University, Guilin 541004, China

出　　处：《Acta Mathematicae Applicatae Sinica》2008年第4期643-648,共6页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(No.10561002);Guangxi Science Foundation(No.0640062);Innovation Project of Guangxi Graduate Education.

摘　　要：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.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 

分 类 号：O17[理学—数学]