数学物理学报(英文版) ›› 1996, Vol. 16 ›› Issue (2): 153-161.
夏明远
Xia Mingyuan
摘要: In this paper we prove that for any prime power q≡3 (mod 8) there exist 4-{q2; k, k, k, k; λ} supplementary difference sets (SDSs) with k=q(q-1)/2, λ=4k-q2,and Hadamard matrices of order 4q2, and give several constructions of these SDSs. Moreover, combining the results of reference[1],we conclude that for any prime p≡3 (mod 8) anti integer τ> 1 there exists an Hadamard matrix of order 4p2r.