A 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 Hadamard matrix of the new order 33396 = 4·8349. Disciplines Physical Sciences and Mathematics Publication Details Seberry, J, A new construction for Williamson-type matrices, Graphs and Combinatorics, 2, 1986, 81-87. This journal article is available at Research Online: http://ro.uow.edu.au/infopapers/1020 Graphs and Combinatorics 2, 81-87 (1986) Graphs alii Combinatorics © Springer_Verlag 1986 A New Construction for Williamson-type Matrices Jennifer Seberry· Department of Computer Science, University of Sydney, N.S.W., 2006, Australia Abstract. It is shown that if q is a prime power then there are Williamson-type matrices of order (i) !q2(q + t) when q == 1 (mod 4), (u) !q2(q + I) when q == 3 (mod 4) and there are Williamson-type matrices of order l(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 Hadamard matrix of the new order 33396 = 4·8349. It is shown that if q is a prime power then there are Williamson-type matrices of order (i) !q2(q + t) when q == 1 (mod 4), (u) !q2(q + I) when q == 3 (mod 4) and there are Williamson-type matrices of order l(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 Hadamard matrix of the new order 33396 = 4·8349.