On quaternary complex Hadamard matrices of small orders

Details On quaternary complex Hadamard matrices of small orders On quaternary complex Hadamard matrices of small orders

2012-04-23

arxiv.org/abs/1204.5160v1

Advances in Mathematics of Communications 5 309--315 (2011)

Mathematics

Combinatorics

7 pages

Scientific paper

10.3934/amc.2011.5.309

One of the main goals of design theory is to classify, characterize and count various combinatorial objects with some prescribed properties. In most cases, however, one quickly encounters a combinatorial explosion and even if the complete enumeration of the objects is possible, there is no apparent way how to study them in details, store them efficiently, or generate a particular one rapidly. In this paper we propose a novel method to deal with these difficulties, and illustrate it by presenting the classification of quaternary complex Hadamard matrices up to order 8. The obtained matrices are members of only a handful of parametric families, and each inequivalent matrix, up to transposition, can be identified through its fingerprint.

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