补差集与Hadamard矩阵

对任何奇素数幂q=2^2 1k 2^s-1(s≥2)构造出了2^s-{q^2,q(q-1);S^s-2q(q-2)P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。

Supplementary difference sets and Hadamard matrices

In this article we obtain 2s-｛q2;q(q-1)/2;2s-2q(q-2)｝ supplementary difference sets(SDSs) for q=2s+1k+2s-1(s≥2), q is a prime power, prove that there exist Hadamard matrices of order 2tq2 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 2tq for t≥s.