✦ LIBER ✦
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.