| had_goethals_T {HadamardR} | R Documentation |
had_goethals_T had_goethals_Turyn performs the Hadamard Matrix from Goethals-Seidel method by using T sequences.
Description
had_goethals_T had_goethals_Turyn performs the Hadamard Matrix from Goethals-Seidel method by using T sequences.
Usage
had_goethals_T(n)
Arguments
n |
integer (order of the matrix) |
Details
This function construct Hadamard matrix of given order using T sequences. If T sequences of length n,n,n,n are available, Hadamard matrix of order 4n can be constructed. Returns the Hadamard matrix of given order. If for given order the T sequences are not available returns NULL.
The T sequences are stored in internal dataset. The available T sequences of length is seq(1,73,2) and 83, 101 and 107
Value
Hadamard matrix of order x
Source
The T sequences are available at London (2013) and 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.
London, S. 2013. Constructing New Turyn Type Sequences, T-Sequences and Hadamard Matrices. PhD Thesis, University of Illinois at Chicago, Chicago.
Examples
had_goethals_T(4)
# [,1] [,2] [,3] [,4]
# [1,] 1 -1 -1 -1
# [2,] 1 1 -1 1
# [3,] 1 1 1 -1
# [4,] 1 -1 1 1
had_goethals_T(8)
#NULL