Hadamard Matrix - Equivalence of Hadamard Matrices

Equivalence of Hadamard Matrices

Two Hadamard matrices are considered equivalent if one can be obtained from the other by negating rows or columns, or by interchanging rows or columns. Up to equivalence, there is a unique Hadamard matrix of orders 1, 2, 4, 8, and 12. There are 5 inequivalent matrices of order 16, 3 of order 20, 60 of order 24, and 487 of order 28. Millions of inequivalent matrices are known for orders 32, 36, and 40. Using a coarser notion of equivalence that also allows transposition, there are 4 inequivalent matrices of order 16, 3 of order 20, 36 of order 24, and 294 of order 28.