cdn_williamson {HadamardR}

cdn_williamson

Description

Checks Hadamard Matrix can be constructed using available Williamson sequences.

Usage

cdn_williamson(order)

Arguments

order

integer

Details

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.

Value

5 or NULL

Source

The Williamson sequences were obtained from Christos Koukouvinos and London (2013).

References

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.

See Also

had_williamson for Williamson construction method using Williamson sequences.

Examples

cdn_williamson(20)
#5
cdn_goethals_T(24)
#NULL