@article{1a08e93554c64613a21aa0eb500e4bc1,
title = "Computation of maximal determinants of binary circulant matrices",
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{\textquoteright}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.",
keywords = "Binary matrix, Booth{\textquoteright}s algorithm, Circulant, Circulant core, Computational imaging, Convolutional Gaussian channel, Difference set, Discrete Mahler measure, Duval{\textquoteright}s algorithm, Hadamard bound, Hadamard matrix, Lyndon word, MURA, Maximal determinant, Modular computation, Necklace, Parallel algorithm, Parallel computation, Quantile estimation, URA",
author = "Brent, {Richard P.} and Yedidia, {Adam B.}",
note = "Publisher Copyright: {\textcopyright} 2018, University of Waterloo. All rights reserved.",
year = "2018",
language = "English",
volume = "21",
journal = "Journal of Integer Sequences",
issn = "1530-7638",
publisher = "University of Waterloo",
number = "5",
}