Ó Catháin, PadraigORCID: 0000-0002-7963-9688 and Wanless, Ian M.ORCID: 0000-0001-8085-0387
(2015)
Trades in complex Hadamard matrices.
In: Algebraic Design Theory and Hadamard Matrices (ADTHM) 2014, 8-11 July 2014, Lethbridge, AB, Canada..
ISBN 978-3-319-17728-1
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 6= 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