Trades in complex hadamard matrices

Padraig O Cathain, Ian Murray Wanless

Research output: Chapter in Book/Report/Conference proceedingChapter (Book)Researchpeer-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 languageEnglish
Title of host publicationAlgebraic Design Theory and Hadamard Matrices
Subtitle of host publicationADTHM, Lethbridge, Alberta, Canada, July 2014
EditorsCharles J Colbourn
Place of PublicationCham Switzerland
PublisherSpringer
Pages213-221
Number of pages9
Volume133
ISBN (Electronic)9783319177298
ISBN (Print)9783319177281
DOIs
Publication statusPublished - 3 Sep 2015
EventWorkshop on Algebraic Design Theory and Hadamard Matrices 2014 - University of Lethbridge, Alberta, Canada
Duration: 8 Jul 201411 Jul 2017
https://link.springer.com/book/10.1007%2F978-3-319-17729-8

Publication series

NameSpringer Proceedings in Mathematics & Statistics
PublisherSpringer
Volume133
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceWorkshop on Algebraic Design Theory and Hadamard Matrices 2014
Abbreviated titleADTHM 2014
CountryCanada
CityAlberta
Period8/07/1411/07/17
Internet address

Keywords

  • Hadamard matrix
  • Trade
  • Rank

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