Butson-type Hadamard matrix


In mathematics, a complex Hadamard matrix H of size N with all its columns mutually orthogonal, belongs to the Butson-type H if all its elements are powers of q-th root of unity,

Existence

If p is prime and, then can exist
only for with integer m and
it is conjectured they exist for all such cases
with. For, the corresponding conjecture is existence for all multiples of 4.
In general, the problem of finding all sets
such that the Butson - type matrices
exist, remains open.

Examples

belong to the Butson-type,