The quaternary complex Hadamard matrices of orders 10, 12, and 14

Details The quaternary complex Hadamard matrices of orders 10, 12, and 14 The quaternary complex Hadamard matrices of orders 10, 12, and 14

2012-04-23

arxiv.org/abs/1204.5164v1

Mathematics

Combinatorics

14+8 pages, preprint

Scientific paper

A complete classification of quaternary complex Hadamard matrices of orders 10, 12 and 14 is given, and a new parametrization scheme for obtaining new examples of affine parametric families of complex Hadamard matrices is provided. On the one hand, it is proven that all 10x10 and 12x12 quaternary complex Hadamard matrices belong to some parametric family, but on the other hand, it is shown by exhibiting an isolated 14x14 matrix that there cannot be a general method for introducing parameters into these types of matrices.

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