Classifying cocyclic Butson Hadamard matrices

Ronan Egan, Dane Flannery, Padraig O Cathain

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Abstract

We classify all the cocyclic Butson Hadamard matrices BH(n,p) of order n over the pth roots of unity for an odd prime p and np ≤ 100. That is, we compile a list of matrices such that any cocyclic BH(n,p) for these n, p is equivalent to exactly one element in the list. Our approach encompasses non-existence results and computational machinery for Butson and generalized Hadamard matrices that are of independent interest.
Original languageEnglish
Title of host publicationAlgebraic Design Theory and Hadamard Matrices: ADTHM, Lethbridge, Alberta, Canada, July 2014
EditorsCharles J Colbourn
Place of PublicationCham Switzerland
PublisherSpringer
Pages93-106
Number of pages14
Volume133
ISBN (Print)9783319177281
DOIs
Publication statusPublished - 2015
EventWorkshop on Algebraic Design Theory and Hadamard Matrices (ADTHM 2014) - University of Lethbridge, Alberta, Canada
Duration: 8 Jul 201411 Jul 2017

Conference

ConferenceWorkshop on Algebraic Design Theory and Hadamard Matrices (ADTHM 2014)
Abbreviated titleADTHM
CountryCanada
CityAlberta
Period8/07/1411/07/17

Keywords

  • Automorphism group
  • Butson hadamard matrix
  • Cocyclic
  • Relative difference set

Cite this

Egan, R., Flannery, D., & O Cathain, P. (2015). Classifying cocyclic Butson Hadamard matrices. In C. J. Colbourn (Ed.), Algebraic Design Theory and Hadamard Matrices: ADTHM, Lethbridge, Alberta, Canada, July 2014 (Vol. 133, pp. 93-106). Cham Switzerland: Springer. https://doi.org/10.1007/978-3-319-17729-8_8