had_goethals_T: had_goethals_T had_goethals_Turyn performs the Hadamard...
In HadamardR: Hadamard Matrix Generation

Description Usage Arguments Details Value Source References Examples

had_goethals_T had_goethals_Turyn performs the Hadamard Matrix from Goethals-Seidel method by using T sequences.

1	had_goethals_T(n)

`n`	integer (order of the matrix)

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

Hadamard matrix of order x

The T sequences are available at London (2013) and 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.

London, S. 2013. Constructing New Turyn Type Sequences, T-Sequences and Hadamard Matrices. PhD Thesis, University of Illinois at Chicago, Chicago.

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