Williamson matrices of order 4n for n=33,35,39
نویسندگان
چکیده
منابع مشابه
Williamson matrices up to order 59
A recent result of Schmidt has brought Williamson matrices back into the spotlight. In this paper a new algorithm is introduced to search for hard to find Williamson matrices. We find all nonequivalent Williamson matrices of odd order n up to n = 59. It turns out that there are none for n = 35, 47, 53, 59 and it seems that the Turyn class may be the only infinite class of these matrices. AMS Su...
متن کاملOn the weighing matrices of order 4n and weight 4n-2 and 2n-1
We algorithms and constructions for mathematical and computer searches which allow us to establish the existence of W( 4n, 4n 2) and 2n 1) for many orders 4n less than 4000. We compare these results with the orders for which W(4n,4n) and W(4n,2n) are known. We use new based on the theory of to obtain new T-matrices of order 43 and J M-matrices which yield W( 4n, 4n 2) for 5,7, 11,13,17,19,25,31...
متن کاملA new construction for Williamson-type matrices
It is shown that if q is a prime power then there are Williamson-type matrices of order (i) 1/2q2(q + 1) when q ≡ 1 (mod 4), (ii)1/4q2(q + 1) when q ≡ 3 (mod 4) and there are Williamson-type matrices of order l/4(q + 1). This gives Williamson-type matrices for the new orders 363, 1183, 1805, 2601, 3174, 5103. The construction can be combined with known results on orthogonal designs to give an H...
متن کاملSome infinite classes of Williamson matrices and weighing matrices
Williamson type matrices A, B, C 1 D will be called nice if ABT + C DT = 0, perfect if ABT + CDT = ACT + BDT 0, special if ABT + CDT = ACT + BDT = ADT + BCT = o. Type 1 (1 , -1 )-matrices A, B, C, D of order n will be called tight Williamson-like matrices if AAT + BBT + CCT + DDT 4nIn and ABT + BAT + CDT + DCT o. Write N = 32T . piTl ••• p!Tn , where Pj 3(mod 4), Pj > 3, j = 1, ... ,n and r, rl...
متن کاملUnified Particle Swarm Optimization for Hadamard matrices of Williamson type
In this work we apply the recently proposed Unified Particle Swarm Optimization (UPSO) method to the search for Hadamard matrices of the Williamson type. The objective functions that arise from the classical Williamson construction, are ideally suited for UPSO algorithms. This is the first time that swarm intelligence methods are applied to this problem. Mathematics Subject Classification (2000...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1993
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)90495-f