had_goethals_base: had_goethals_base
In HadamardR: Hadamard Matrix Generation

Description Usage Arguments Details Value Source References Examples

had_goethals_base performs the construction of Hadamard Matrix from Goethals-Seidel method. by using the Base sequences.

1	had_goethals_base(x)

`x`	integer (order of the matrix)

This function construct the Hadamard matrix of given order using base sequences. If base sequences of length n+1,n+1,n,n are available, base sequences are converted into T-sequences of length 2n+1,2n+1,2n+1,2n+1 can be constructed. From T-sequence of length 2n+1, Hadamard matrix of order 4(2n+1) can be constructed. For a given order the base sequences is not available it returns NULL.

The Base sequences are stored in internal dataset. The available Base sequences of length is 1,2,3,4,.....,35

Hadamard matrix of order x

The Base sequences were obtained from Christos Koukouvinos

Goethals, J. M. and Seidel, J. J. (1967). Orthogonal matrices with zero diagnol. Canad. J. Math., 19, 259-264.

had_goethals_base(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
had_goethals_base(16)
#NULL