补差集与Hadamard矩阵

Supplementary difference sets and Hadamard matrices

对任何奇素数幂 q=2 s+ 1 k +2 s -1 ( s≥ 2 )构造出了 2 s-{q2 ;q( q-1 ) / 2 ;2 s- 2 q( q -2 ) }补差集 ,证明了存在 2 tq2 阶 Hadamard矩阵 ( t≥ s) ,并且对任何奇自然数 q证明了存在 s=s( q) ,对任意 t≥ s存在 2 tq阶 Hadamard矩阵 .

In this article we obtain 2 s ｛q 2;q(q-1)/2;2 s-2 q(q-2)｝ supplementary difference sets(SDSs) for q=2 s+1 k+2 s-1(s≥2), q is a prime power, prove that there exist Hadamard matrices of order 2 tq 2 for t≥s. Let q be any odd number. We prove that there exists a s=s(q) so that there is an Hadamard matrix of order 2 tq for t≥s.