| Description |
Usage:
H = paleyI(N);
N: order of the Hadamard matrix to be computed (integer)
H: returns the computed Hadamard matrix or returns 0 if an error occurred (invalid matrix order or incorrect H-matrix)
H-matrices of Paley type I are defined for orders N = 4m = p+1 (m=1,2,3,...), where p is a prime with mod(p,4)=3, i.e. N=12, 20, 44, 60, 68, 72, 84, ... (In this list valid Paley type I matrix orders that are equal to N=2^n (n=1,2,3,...) are omitted).
H-matrices contain only '+1' and '-1' elements and are orthogonal.
The first row and column of a Paley type I H-matrix consists only of '+1' elements. All diagonal elements H(l,m) with l=m~=1 are equal to '-1'. The determination of all other elements is based on evaluating the Legendre symbol,
which is defined to be equal to '+1' or '-1' if its argument is a quadratic residue or a quadratic non-residue. |
