File Exchange

image thumbnail

Paley Type I Hadamard matrices

version 1.0.0.0 (1.22 KB) by Gernot Berger
Computes Hadamard matrices (H-matrices) of Paley Type I

3 Downloads

Updated 02 Jul 2008

No License

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.

Cite As

Gernot Berger (2021). Paley Type I Hadamard matrices (https://www.mathworks.com/matlabcentral/fileexchange/20527-paley-type-i-hadamard-matrices), MATLAB Central File Exchange. Retrieved .

Comments and Ratings (1)

Thomas Stemler

MATLAB Release Compatibility
Created with R14SP1
Compatible with any release
Platform Compatibility
Windows macOS Linux

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!