On higher dimensional cocyclic Hadamard matrices

Provided that a cohomological model for G is known, we describe a method for constructing a basis for n -cocycles over G , from which the whole set of n -dimensional n -cocyclic matrices over G may be straightforwardly calculated. Focusing in the case n = 2 (which is of special interest, e.g. for lo...

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Bibliographic Details
Published in:Applicable algebra in engineering, communication and computing communication and computing, 2015-03, Vol.26 (1-2), p.191-206
Main Authors: Álvarez, V., Armario, J. A., Frau, M. D., Real, P.
Format: Article
Language:English
Subjects:
Artificial Intelligence
Computer Hardware
Computer Science
Original Paper
Symbolic and Algebraic Manipulation
Theory of Computation
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Summary:Provided that a cohomological model for G is known, we describe a method for constructing a basis for n -cocycles over G , from which the whole set of n -dimensional n -cocyclic matrices over G may be straightforwardly calculated. Focusing in the case n = 2 (which is of special interest, e.g. for looking for cocyclic Hadamard matrices), this method provides a basis for 2-cocycles in such a way that representative 2 -cocycles are calculated all at once, so that there is no need to distinguish between inflation and transgression 2-cocycles (as it has traditionally been the case until now). When n > 2 , this method provides an uniform way of looking for higher dimensional n-cocyclic Hadamard matrices for the first time. We illustrate the method with some examples, for n = 2 , 3 . In particular, we give some examples of improper 3-dimensional 3 -cocyclic Hadamard matrices.
ISSN:0938-1279
1432-0622
DOI:10.1007/s00200-014-0242-3