Published January 22, 2018 | Version v1
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(Pseudo)-cocyclic (structured) Hadamard matrices over (quasi)groups

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Progressing on a survey of the state of the art of cocyclic constructions for Hadamard matrices, we will prove that the family of Goethals-Seidel Hadamard matrices is (pseudo)-cocyclic over a certain family of quasigroups. Therefore, what we call (pseudo)-cocyclic (structured) Hadamard matrices over (quasi)groups, precisely those matrices satisfying some kind of cocycle Hadamard test known so far, include most of the well-known and prolific constructions of Hadamard matrices. We will discuss also different approaches in order to look for large matrices of this type.

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https://idus.us.es/handle//11441/69270
URN
urn:oai:idus.us.es:11441/69270

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