HadamardMat improvements

[osj1961]

There is a paper, DISCOVERY OF AN HADAMARD MATRIX OF ORDER 92 by LEONARD BAUMERT, S. W. GOLOMB AND MARSHALL HALL, JR. describing a construction using a 4x4 block form

[  A  B  C  D ]
[ -B  A -D  C ]
[ -C  D  A -B ]
[ -D -C  B  A ]

where A,B,C & D are 23x23 (symmetric) circulant matrices.

They claim the method can be generalized to cover 92, 116, 156, and 188 (also 172 which was originally done by J. Williamson using "a special automorphism of order 3") The amount of computation involved was apparently prohibitive in 1961. The technique may have to do with finding multiple difference sets in
GF(m/4).

[osj1961]

Found another paper, Hadamard Matrices of the Williamson Type
By L. D. Baumert and Marshall Hall, Jr. w/ more details. The first rows of the circulant matrices correspond to solutions of x^2+y^2+z^2+w^2=4t in odd integers but written in terms of polynomials in
$\omega_i$ which is left undefined...

[osj1961]

Neil Sloan maintains a webpage about Hadamard matrices:
http://neilsloane.com/hadamard/index.html
where in addition to Williamson type he also mentions Turyn type.
There are several references...