Brent, RichardYedidia, Adam B.2023-03-091530-7638http://hdl.handle.net/1885/286948We 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.application/pdfen-AU© 2018 The Author(s)binary matrixBooth’s algorithmcirculantcirculant corecomputational imagingconvolutional Gaussian channeldifference setdiscrete Mahler measureDuval’s algorithmHadamard boundHadamard matrixLyndon wordmaximal determinantmodular computationMURAnecklaceparallel algorithmparallel computationquantile estimationURA20182021-12-26