PaleyII: PaleyII

In HadamardR: Hadamard Matrix Generation

Description

This function create the Hadamard matrix by Paley method 2

Usage

PaleyII(n)

Arguments

n	integer(order of the matrix)

Details

q=n/2-1, If there is an Hadamard matrix of order h>1, and q = 1 (mod 4) is a prime number, then there exists an Hadamard matrix of order nh.

Value

Hadamard matrix of order n

References

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

Examples

PaleyII(12)
#      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
# [1,]    1    1    1    1    1    1    1   -1   -1    -1    -1    -1
# [2,]    1    1    1   -1   -1    1   -1    1   -1     1     1    -1
# [3,]    1    1    1    1   -1   -1   -1   -1    1    -1     1     1
# [4,]    1   -1    1    1    1   -1   -1    1   -1     1    -1     1
# [5,]    1   -1   -1    1    1    1   -1    1    1    -1     1    -1
# [6,]    1    1   -1   -1    1    1   -1   -1    1     1    -1     1
# [7,]    1   -1   -1   -1   -1   -1   -1   -1   -1    -1    -1    -1
# [8,]   -1    1   -1    1    1   -1   -1   -1   -1     1     1    -1
# [9,]   -1   -1    1   -1    1    1   -1   -1   -1    -1     1     1
#[10,]   -1    1   -1    1   -1    1   -1    1   -1    -1    -1     1
#[11,]   -1    1    1   -1    1   -1   -1    1    1    -1    -1    -1
#[12,]   -1   -1    1    1   -1    1   -1   -1    1     1    -1    -1
PaleyII(8)
#NULL

Example output

      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
 [1,]    1    1    1    1    1    1    1   -1   -1    -1    -1    -1
 [2,]    1    1    1   -1   -1    1   -1    1   -1     1     1    -1
 [3,]    1    1    1    1   -1   -1   -1   -1    1    -1     1     1
 [4,]    1   -1    1    1    1   -1   -1    1   -1     1    -1     1
 [5,]    1   -1   -1    1    1    1   -1    1    1    -1     1    -1
 [6,]    1    1   -1   -1    1    1   -1   -1    1     1    -1     1
 [7,]    1   -1   -1   -1   -1   -1   -1   -1   -1    -1    -1    -1
 [8,]   -1    1   -1    1    1   -1   -1   -1   -1     1     1    -1
 [9,]   -1   -1    1   -1    1    1   -1   -1   -1    -1     1     1
[10,]   -1    1   -1    1   -1    1   -1    1   -1    -1    -1     1
[11,]   -1    1    1   -1    1   -1   -1    1    1    -1    -1    -1
[12,]   -1   -1    1    1   -1    1   -1   -1    1     1    -1    -1
NULL

HadamardR documentation built on April 14, 2020, 7:01 p.m.