数学物理学报(英文版) ›› 1995, Vol. 15 ›› Issue (4): 361-369.
• Articles • 下一篇
夏明远1, 刘钢2
Xia Mingyuan1, Liu Gang2
摘要: An infinite family of H1 is obtained, that is,H1(ν)≠∅ for υ ∈ N=N1 ∪ N2 ∪ N3 where
N1={5,13,17,25,37,41,61},N2{υ=32r(p1r…pxr)4:p1≡3(mod 4)prime,p1>3,r,r1≥0,i=1,2,…,n;n=1,2,…},N3={υ1υ2:υ1∈N1 and υ2∈N2}. Using H1(υ),we give 2-(2υ;k1,k2;k1 + k2 -υ} supplementary difference sets with υ=(k1-υ)2 + (k2-υ)2. Finally. we prove that if there exists an orthogonal design OD(4t;t,t,t,t) and H1(υ) ≠∅ then a Hadamard matrix of order 4tυ can be constructed.