PaleyI {HadamardR}

PaleyI

Description

This function performs constructing the Hadamard matrix by Paley method.

Usage

PaleyI(n)

Arguments

n

integer (order of the matrix)

Details

let q = n-1 , and q = 3 (mod 4), q is the prime number, then obtained the Hadamard matrix of order q+1.if input satisfies these condition it retuns Hadamard Matrix; otherwise returns NULL.

Value

hadamard matrix of n

References

Paley, R.E.A.C. (1933). On Orthogonal matrices. J. Combin. Theory, A 57(1), 86-108.

Examples

PaleyI(8)
#' PaleyI(8)
#      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#[1,]    1    1    1    1    1    1    1    1
#[2,]   -1    1   -1   -1    1   -1    1    1
#[3,]   -1    1    1   -1   -1    1   -1    1
#[4,]   -1    1    1    1   -1   -1    1   -1
#[5,]   -1   -1    1    1    1   -1   -1    1
#[6,]   -1    1   -1    1    1    1   -1   -1
#[7,]   -1   -1    1   -1    1    1    1   -1
#[8,]   -1   -1   -1    1   -1    1    1    1
PaleyI(16)
#NULL