Trades in complex hadamard matrices

Padraig O Cathain; Ian Murray Wanless

doi:10.1007/978-3-319-17729-8_18

Trades in complex hadamard matrices

Padraig O Cathain, Ian Murray Wanless

School of Mathematics

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

2 Citations (Scopus)

Abstract

A trade in a complex Hadamard matrix is a set of entries which can be changed to obtain a different complex Hadamard matrix. We show that in a real Hadamard matrix of order n all trades contain at least n entries. We call a trade rectangular if it consists of a submatrix that can be multiplied by some scalar c ≠ 1 to obtain another complex Hadamard matrix. We give a characterisation of rectangular trades in complex Hadamard matrices of order n and show that they all contain at least n entries. We conjecture that all trades in complex Hadamard matrices contain at least n entries.

Original language	English
Title of host publication	Algebraic Design Theory and Hadamard Matrices
Subtitle of host publication	ADTHM, Lethbridge, Alberta, Canada, July 2014
Editors	Charles J Colbourn
Place of Publication	Cham Switzerland
Publisher	Springer
Pages	213-221
Number of pages	9
Volume	133
ISBN (Electronic)	9783319177298
ISBN (Print)	9783319177281
DOIs	https://doi.org/10.1007/978-3-319-17729-8_18
Publication status	Published - 3 Sept 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

Publication series

Name	Springer Proceedings in Mathematics & Statistics
Publisher	Springer
Volume	133
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	Workshop on Algebraic Design Theory and Hadamard Matrices 2014
Abbreviated title	ADTHM 2014
Country/Territory	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

Hadamard matrix
Trade
Rank

Access to Document

10.1007/978-3-319-17729-8_18

Cite this

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title = "Trades in complex hadamard matrices",

abstract = "A trade in a complex Hadamard matrix is a set of entries which can be changed to obtain a different complex Hadamard matrix. We show that in a real Hadamard matrix of order n all trades contain at least n entries. We call a trade rectangular if it consists of a submatrix that can be multiplied by some scalar c ≠ 1 to obtain another complex Hadamard matrix. We give a characterisation of rectangular trades in complex Hadamard matrices of order n and show that they all contain at least n entries. We conjecture that all trades in complex Hadamard matrices contain at least n entries.",

keywords = "Hadamard matrix, Trade, Rank",

author = "{O Cathain}, Padraig and Wanless, {Ian Murray}",

year = "2015",

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doi = "10.1007/978-3-319-17729-8_18",

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pages = "213--221",

editor = "Colbourn, {Charles J}",

booktitle = "Algebraic Design Theory and Hadamard Matrices",

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

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O Cathain, P & Wanless, IM 2015, Trades in complex hadamard matrices. in CJ Colbourn (ed.), Algebraic Design Theory and Hadamard Matrices: ADTHM, Lethbridge, Alberta, Canada, July 2014. vol. 133, Springer Proceedings in Mathematics & Statistics, vol. 133, Springer, Cham Switzerland, pp. 213-221, Workshop on Algebraic Design Theory and Hadamard Matrices 2014, Alberta, British Columbia, Canada, 8/07/14. https://doi.org/10.1007/978-3-319-17729-8_18

Trades in complex hadamard matrices. / O Cathain, Padraig; Wanless, Ian Murray.
Algebraic Design Theory and Hadamard Matrices: ADTHM, Lethbridge, Alberta, Canada, July 2014. ed. / Charles J Colbourn. Vol. 133 Cham Switzerland: Springer, 2015. p. 213-221 (Springer Proceedings in Mathematics & Statistics; Vol. 133).

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

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N2 - A trade in a complex Hadamard matrix is a set of entries which can be changed to obtain a different complex Hadamard matrix. We show that in a real Hadamard matrix of order n all trades contain at least n entries. We call a trade rectangular if it consists of a submatrix that can be multiplied by some scalar c ≠ 1 to obtain another complex Hadamard matrix. We give a characterisation of rectangular trades in complex Hadamard matrices of order n and show that they all contain at least n entries. We conjecture that all trades in complex Hadamard matrices contain at least n entries.

AB - A trade in a complex Hadamard matrix is a set of entries which can be changed to obtain a different complex Hadamard matrix. We show that in a real Hadamard matrix of order n all trades contain at least n entries. We call a trade rectangular if it consists of a submatrix that can be multiplied by some scalar c ≠ 1 to obtain another complex Hadamard matrix. We give a characterisation of rectangular trades in complex Hadamard matrices of order n and show that they all contain at least n entries. We conjecture that all trades in complex Hadamard matrices contain at least n entries.

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KW - Rank

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ER -

Trades in complex hadamard matrices

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Towards the prime power conjecture

Extremal Problems in Hypergraph Matchings

Cite this

Trades in complex hadamard matrices

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Projects

Towards the prime power conjecture

Extremal Problems in Hypergraph Matchings

Cite this