A path to hadamard matrices

Authors:
P. Embury;A. Rao
Affiliations:
School of Mathematics and Geospatial Sciences, RMIT University, Melbourne, Australia;School of Mathematics and Geospatial Sciences, RMIT University, Melbourne, Australia
Venue:
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Year:
2007

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Abstract

There are characteristics of Hadamard matrices that enable an exhaustive search using algorithmic techniques. The search derives primarily from the eigenvalues which are constant after the Hadamard matrix is multiplied by its transpose. Generally this would be a performance concern but there are additional properties that enable the eigenvalues to be predicted. Here an algorithm is given to obtain a Hadamard matrix from a matrix of 1s using optimisation techniques on a row-by-row basis.