Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivalences of ${\mathbb Z} _t \times {\mathbb Z}_2^2$-cocyclic
  Hadamard matrices   One of the most promising structural approaches to resolving the Hadamard
Conjecture uses the family of cocyclic matrices over ${\mathbb Z} _t \times
{\mathbb Z}_2^2$. Two types of equivalence relations for classifying cocyclic
matrices over ${\mathbb Z} _t \times {\mathbb Z}_2^2$ have been found. Any
cocyclic matrix equivalent by either of these relations to a Hadamard matrix
will also be Hadamard.
  One type, based on algebraic relations between cocycles over any finite
group, has been known for some time. Recently, and independently, a second
type, based on four geometric relations between diagrammatic visualisations of
cocyclic matrices over ${\mathbb Z} _t \times {\mathbb Z}_2^2$, has been found.
Here we translate the algebraic equivalences to diagrammatic equivalences and
show one of the diagrammatic equivalences cannot be obtained this way. This
additional equivalence is shown to be the geometric translation of matrix
transposition.

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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: stat