Hadamard matrices of orders 116 and 232

Five new orders for Hadamard matrices of skew type

By using the (generalized) Goethals-Seidel array, we construct Hadamard matrices of skew type of order 4n for n = 81,103,151,169, and 463. Hadamard matrices of skew type for these orders are constructed here for the first time. Consequently the list of odd integers n < 300 for which no Hadamard matrix of skew type of order 4n is presently known is reduced to 45 numbers (see the comments after t...

New restrictions on possible orders of circulant Hadamard matrices

We obtain several new number theoretic results which improve the field descent method. We use these results to rule out many of the known open cases of the circulant Hadamard matrix conjecture. In particular, the only known open case of the Barker sequence conjecture is settled.

Jacket matrices constructed from Hadamard matrices and generalized Hadamard matrices

Hadamard and Conference Matrices

We discuss new constructions of Hadamard and conference matrices using relative difference sets. We present the first example of a relative (n, 2, n − 1, n−2 2 )-difference set where n − 1 is not a prime power.

Entropy and Hadamard Matrices

The entropy of an orthogonal matrix is defined. It provides a new interpretation of Hadamard matrices as those that saturate the bound for entropy. It appears to be a useful Morse function on the group manifold. It has sharp maxima and other saddle points. The matrices corresponding to the maxima for 3 and 5 dimensions are presented. They are integer matrices (upto a rescaling.)