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© Birkhäuser Verlag Basel/Switzerland 2009 Annals of Combinatorics Weighing Matrices and String Sorting

By Ilias S. Kotsireas, Christos Koukouvinos, Jennifer Seberry Department Of Physics and Computer Science


Abstract. In this paper we establish a fundamental link between the search for weighing matrices constructed from two circulants and the operation of sorting strings, an operation that has been studied extensively in computer science. In particular, we demonstrate that the search for weighing matrices constructed from two circulants using the power spectral density criterion and exploiting structural patterns for the locations of the zeros in candidate solutions, can be viewed as a string sorting problem together with a linear time algorithm to locate common strings in two sorted arrays. This allows us to bring into bear efficient algorithms from the string sorting literature. We also state and prove some new enhancements to the power spectral density criterion, that allow us to treat successfully the rounding error effect and speed up the algorithm. Finally, we use these ideas to find new weighing matrices of order 2n and weights 2n − 13, 2n − 17 constructed from two circulants

Topics: weighing matrices, algorithm, pattern, locations of zeros, power spectral density, rounding
Year: 2007
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