Computation of Maximal Determinants of Binary Circulant Matrices
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Brent, Richard
Yedidia, Adam B.
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University of Waterloo
Abstract
We describe algorithms for computing maximal determinants of binary circulant matrices of small orders. Here "binary matrix" means a matrix whose elements are drawn from {0, 1} or {-1, 1}. We describe efficient parallel algorithms for the search, using Duval's algorithm for generation of necklaces and the well-known representation of the determinant of a circulant in terms of roots of unity. Tables of maximal determinants are given for orders <= 52. Our computations extend earlier results and disprove two plausible conjectures.
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binary matrix, Booth’s algorithm, circulant, circulant core, computational imaging, convolutional Gaussian channel, difference set, discrete Mahler measure, Duval’s algorithm, Hadamard bound, Hadamard matrix, Lyndon word, maximal determinant, modular computation, MURA, necklace, parallel algorithm, parallel computation, quantile estimation, URA
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Journal of Integer Sequences
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2099-12-31
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