Description Usage Arguments Details Value Source References See Also Examples
View source: R/cdn_williamson.R
Checks Hadamard Matrix can be constructed using available Williamson sequences.
1 |
order |
integer |
This function checks whether the Hadamard matrix of given order can be constructed using williamson sequences. If Williamson sequences of length n,n,n,n are available, Hadamard matrix of order 4n can be constructed. Returns the value 5, if it is possible otherwise NULL is returned.
Williamson sequences are available for length of seq(1,63, 2) except 15, 35, 47, 53, 59 in the internal table.
5 or NULL
The Williamson sequences were obtained from Christos Koukouvinos and London (2013).
Williamson, J. (1944). Hadamard determinant theorem and the sum of four squares. Duke. Math. J., 11, 65-81.
Williamson, J. (1947). Note on Hadamard's determnant theorem. Bull. Amer. Math. Soc., 53, 608-613.
London, S. 2013. Constructing New Turyn Type Sequences, T-Sequences and Hadamard Matrices. PhD Thesis, University of Illinois at Chicago, Chicago.
had_williamson
for Williamson construction method using Williamson sequences.
1 2 3 4 | cdn_williamson(20)
#5
cdn_goethals_T(24)
#NULL
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