华中师范大学学报(自然科学版)
華中師範大學學報(自然科學版)
화중사범대학학보(자연과학판)
JOURNAL OF CENTRAL CHINA NORMAL UNIVERSITY
2001年
2期
132-135
,共4页
Abelian群%特征标%φ函数%补差集%Hadamard矩阵
Abelian群%特徵標%φ函數%補差集%Hadamard矩陣
Abelian군%특정표%φ함수%보차집%Hadamard구진
对任何奇素数幂q=2s+1k+2s-1(s≥2)构造出了2s-{q2;q(q-1)/2;2s-2q(q-2)｝补差集, 证明了存在2tq2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2tq阶Hadamard矩阵.
對任何奇素數冪q=2s+1k+2s-1(s≥2)構造齣瞭2s-{q2;q(q-1)/2;2s-2q(q-2)｝補差集, 證明瞭存在2tq2階Hadamard矩陣(t≥s), 併且對任何奇自然數q證明瞭存在s=s(q), 對任意t≥s存在2tq階Hadamard矩陣.
대임하기소수멱q=2s+1k+2s-1(s≥2)구조출료2s-{q2;q(q-1)/2;2s-2q(q-2)｝보차집, 증명료존재2tq2계Hadamard구진(t≥s), 병차대임하기자연수q증명료존재s=s(q), 대임의t≥s존재2tq계Hadamard구진.
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.
