Classifying cocyclic Butson Hadamard matrices

Ronan Egan; Dane Flannery; Padraig O Cathain

doi:10.1007/978-3-319-17729-8_8

Classifying cocyclic Butson Hadamard matrices

Ronan Egan, Dane Flannery, Padraig O Cathain

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

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 language	English
Title of host publication	Algebraic Design Theory and Hadamard Matrices: ADTHM, Lethbridge, Alberta, Canada, July 2014
Editors	Charles J Colbourn
Place of Publication	Cham Switzerland
Publisher	Springer
Pages	93-106
Number of pages	14
Volume	133
ISBN (Print)	9783319177281
DOIs	https://doi.org/10.1007/978-3-319-17729-8_8
Publication status	Published - 2015
Event	Workshop on Algebraic Design Theory and Hadamard Matrices 2014 - University of Lethbridge, Alberta, Canada Duration: 8 Jul 2014 → 11 Jul 2017 https://link.springer.com/book/10.1007%2F978-3-319-17729-8

Conference

Conference	Workshop on Algebraic Design Theory and Hadamard Matrices 2014
Abbreviated title	ADTHM 2014
Country	Canada
City	Alberta
Period	8/07/14 → 11/07/17
Internet address	https://link.springer.com/book/10.1007%2F978-3-319-17729-8

Keywords

Automorphism group
Butson hadamard matrix
Cocyclic
Relative difference set

Access to Document

10.1007/978-3-319-17729-8_8

Cite this

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title = "Classifying cocyclic Butson Hadamard matrices",

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.",

keywords = "Automorphism group, Butson hadamard matrix, Cocyclic, Relative difference set",

author = "Ronan Egan and Dane Flannery and {O Cathain}, Padraig",

year = "2015",

doi = "10.1007/978-3-319-17729-8_8",

language = "English",

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volume = "133",

pages = "93--106",

editor = "Colbourn, {Charles J}",

booktitle = "Algebraic Design Theory and Hadamard Matrices: ADTHM, Lethbridge, Alberta, Canada, July 2014",

publisher = "Springer",

note = "Workshop on Algebraic Design Theory and Hadamard Matrices 2014, ADTHM 2014 ; Conference date: 08-07-2014 Through 11-07-2017",

url = "https://link.springer.com/book/10.1007%2F978-3-319-17729-8",

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Egan, R, Flannery, D & O Cathain, P 2015, Classifying cocyclic Butson Hadamard matrices. in CJ Colbourn (ed.), Algebraic Design Theory and Hadamard Matrices: ADTHM, Lethbridge, Alberta, Canada, July 2014. vol. 133, Springer, Cham Switzerland, pp. 93-106, Workshop on Algebraic Design Theory and Hadamard Matrices 2014, Alberta, Canada, 8/07/14. https://doi.org/10.1007/978-3-319-17729-8_8

Classifying cocyclic Butson Hadamard matrices. / Egan, Ronan; Flannery, Dane; O Cathain, Padraig.

Algebraic Design Theory and Hadamard Matrices: ADTHM, Lethbridge, Alberta, Canada, July 2014. ed. / Charles J Colbourn. Vol. 133 Cham Switzerland : Springer, 2015. p. 93-106.

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

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T1 - Classifying cocyclic Butson Hadamard matrices

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AU - Flannery, Dane

AU - O Cathain, Padraig

PY - 2015

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N2 - 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.

AB - 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.

KW - Automorphism group

KW - Butson hadamard matrix

KW - Cocyclic

KW - Relative difference set

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DO - 10.1007/978-3-319-17729-8_8

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BT - Algebraic Design Theory and Hadamard Matrices: ADTHM, Lethbridge, Alberta, Canada, July 2014

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