@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",

}