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Hadamard matrices constructed from supplementary difference sets in the class ℋ1

✍ Scribed by Ming-Yuan Xia; Tian-Bing Xia


Publisher
John Wiley and Sons
Year
1994
Tongue
English
Weight
385 KB
Volume
2
Category
Article
ISSN
1063-8539

No coin nor oath required. For personal study only.

✦ Synopsis


In this article we give the definition of the class N = NI U N z U 3 f 3 where and prove: (1) 3 f l ( v ) # 4 for v E 3fl = { p 2 r : p = S(mod 8) a prime, T f O(mod 4)}, NZ = {3"( p ; --. P : ) ~: pi = 3(mod 4) a prime, pi > 3 , r,ri 2 0, i = l , ---, n ; n = 1,2,-*.}, N 3 = {vv': v E N 1 and v ' E N 2 } ;

(2) there exists 2 -{2qz; q2 f q, 4'; q2 f q } supplementary difference sets for q2 E N ;

(3) there exists an Hadamard matrix of order 4v for v E N ; (4) if t is an order of T-matrices, there exists an Hadamard matrix of order 4 h for v E 3 f . 0 1994 John Wiley & Sons, Inc.