组大小为16的广义斯坦纳三元系(英文)

Generalized Steiner triple systems with group size sixteen

广义斯坦纳三元系GS(2,3,n,g)等价于g+1元最优常重量码(n,3,3).证明了GS(2,3,n,16)存在的必要条件n≡0,1(mod 3),n≥18也是充分的.

Abstract： Generalized Steiner triple systems, GS （ 2,3, n, g） are equivalent to （ g ＋ 1 ） -ary （ n, 3,3 ） maximum con- st,ant weight codes. In this paper,it is proved that the necessary conditions for the existence of a GS （ 2,3, n, 16 ）, namely, n = 0,1 （ mod 3 ） and n 1〉 18, are also sufficient.