Trades in complex Hadamard matrices
Combinatorics
2015-12-17 v1
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 all trades contain at least entries. We call a trade rectangular if it consists of a submatrix that can be multiplied by some scalar to obtain another complex Hadamard matrix. We give a characterisation of rectangular trades in complex Hadamard matrices of order and show that they all contain at least entries. We conjecture that all trades in complex Hadamard matrices contain at least entries.
Keywords
Cite
@article{arxiv.1502.02353,
title = {Trades in complex Hadamard matrices},
author = {Padraig Ó Catháin and Ian M. Wanless},
journal= {arXiv preprint arXiv:1502.02353},
year = {2015}
}
Comments
9 pages, no figures