广义Steiner三元系(英文)

Generalized Steiner Triple Systems

一个广义 Steiner三元系 GS( 2 ,3,n,g)等价于一个最大常重量码 ,字符取自一个 g+ 1元集 ,码字长为 n,距离为 3,重量为 3.介绍一种特殊可分组设计 ( K-* GDD) ,用 Wilson关于可分组设计的基本构造法来构造广义 Steiner三元系 .特别对 g=4 ,证明了一个广义 Steiner三元系 GS( 2 ,3,n,g)的几个必要条件是充分的 .

Generalized Steiner triple systems, GS (2,3,n,g) are equivalent to maximum constant weight codes over an alphabet of size g+1 with distance 3 and weight 3 in which each codeword has length n . By introducing a special kind of group divisible design (denoted K- * GDD), Wilson′s Fundamental Construction for GDDs is used to construct generalized Steiner triple systems. The numerical necessary conditions for the existance of a GS (2,3,n,g) are shown to be sufficient for g=4 .