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.
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CITATION STYLE
Catháin, P., & Wanless, I. M. (2015). Trades in complex hadamard matrices. In Algebraic Design Theory and Hadamard Matrices: ADTHM, Lethbridge, Alberta, Canada, July 2014 (Vol. 133, pp. 213–221). Springer International Publishing. https://doi.org/10.1007/978-3-319-17729-8_18
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