Order 24 Hadamard matrices of character at least 3

Hadamard matrices of order 32

Two Hadamard matrices are considered equivalent if one is obtained from the other by a sequence of operations involving row or column permutations or negations. We complete the classification of Hadamard matrices of order 32. It turns out that there are exactly 13710027 such matrices up to equivalence. AMS Subject Classification: 05B20, 05B05, 05B30.

Hadamard matrices of order 764 exist

Two Hadamard matrices of order 764 of Goethals– Seidel type are constructed. Recall that a Hadamard matrix of order m is a {±1}-matrix A of size m × m such that AA T = mI m , where T denotes the transpose and I m the identity matrix. We refer the reader to one of [2, 4] for the survey of known results about Hadamard matrices. In our previous note [1], written about 13 years ago, we listed 17 in...

On Hadamard Matrices at Roots of Unity

Abstract. We study Hadamard matrices of order n, formed by l-th roots of unity. A main problem is to find the allowed values of (n, l), and we discuss here the following statement: for l = pa 1 . . . pa s we must have n ∈ p1+. . .+psN. For s = 1 this is a previously known result, for s = 2, 3 this is a result that we prove in this paper, and for s ≥ 4 this is a conjecture that we raise. We pres...

Jacket matrices constructed from Hadamard matrices and generalized Hadamard matrices

On the classification of Hadamard matrices of order 32

All equivalence classes of Hadamard matrices of order at most 28 have been found by 1994. Order 32 is where a combinatorial explosion occurs on the number of inequivalent Hadamard matrices. We find all equivalence classes of Hadamard matrices of order 32 which are of certain types. It turns out that there are exactly 13,680,757 Hadamard matrices of one type and 26,369 such matrices of another t...