Computation of Maximal Determinants of Binary Circulant Matrices

01/01/2018

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by   Richard P. Brent, et al.

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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 Lyndon words and the well-known representation of the determinant of a circulant in terms of roots of unity. Our computations extend earlier results and disprove two plausible conjectures.