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Computation of Maximal Determinants of Binary Circulant Matrices

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dc.contributor.authorBrent, Richard
dc.contributor.authorYedidia, Adam B.
dc.date.accessioned2023-03-09T22:41:40Z
dc.date.issued2018
dc.date.updated2021-12-26T07:19:13Z
dc.description.abstractWe 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.en_AU
dc.format.mimetypeapplication/pdfen_AU
dc.identifier.issn1530-7638en_AU
dc.identifier.urihttp://hdl.handle.net/1885/286948
dc.language.isoen_AUen_AU
dc.publisherUniversity of Waterlooen_AU
dc.rights© 2018 The Author(s)en_AU
dc.sourceJournal of Integer Sequencesen_AU
dc.subjectbinary matrixen_AU
dc.subjectBooth’s algorithmen_AU
dc.subjectcirculanten_AU
dc.subjectcirculant coreen_AU
dc.subjectcomputational imagingen_AU
dc.subjectconvolutional Gaussian channelen_AU
dc.subjectdifference seten_AU
dc.subjectdiscrete Mahler measureen_AU
dc.subjectDuval’s algorithmen_AU
dc.subjectHadamard bounden_AU
dc.subjectHadamard matrixen_AU
dc.subjectLyndon worden_AU
dc.subjectmaximal determinanten_AU
dc.subjectmodular computationen_AU
dc.subjectMURAen_AU
dc.subjectnecklaceen_AU
dc.subjectparallel algorithmen_AU
dc.subjectparallel computationen_AU
dc.subjectquantile estimationen_AU
dc.subjectURAen_AU
dc.titleComputation of Maximal Determinants of Binary Circulant Matricesen_AU
dc.typeJournal articleen_AU
local.bibliographicCitation.issue5en_AU
local.bibliographicCitation.lastpage19en_AU
local.bibliographicCitation.startpage1en_AU
local.contributor.affiliationBrent, Richard, College of Science, ANUen_AU
local.contributor.affiliationYedidia, Adam B., Massachusetts Institute of Technologyen_AU
local.contributor.authoruidBrent, Richard, u4241028en_AU
local.description.embargo2099-12-31
local.description.notesImported from ARIESen_AU
local.identifier.absfor490404 - Combinatorics and discrete mathematics (excl. physical combinatorics)en_AU
local.identifier.absseo280118 - Expanding knowledge in the mathematical sciencesen_AU
local.identifier.ariespublicationu3102795xPUB2844en_AU
local.identifier.citationvolume21en_AU
local.identifier.thomsonIDWOS:000438431500006
local.publisher.urlhttps://cs.uwaterloo.ca/journals/JIS/en_AU
local.type.statusPublished Versionen_AU

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