| had_goethals_base {HadamardR} | R Documentation |
had_goethals_base
Description
had_goethals_base performs the construction of Hadamard Matrix from Goethals-Seidel method. by using the Base sequences.
Usage
had_goethals_base(x)
Arguments
x |
integer (order of the matrix) |
Details
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
Value
Hadamard matrix of order x
Source
The Base sequences were obtained from Christos Koukouvinos
References
Goethals, J. M. and Seidel, J. J. (1967). Orthogonal matrices with zero diagnol. Canad. J. Math., 19, 259-264.
Examples
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