On Zt x Z2,2-cocyclic Hadamard matrices

Details On Zt x Z2,2-cocyclic Hadamard matrices On Zt x Z2,2-cocyclic Hadamard matrices

2011-12-19

arxiv.org/abs/1112.4296v1

Mathematics

Combinatorics

17 pages, 1 figure

Scientific paper

A characterization of Zt x Z2,2-cocyclic Hadamard matrices is described, depending on the notions of distributions, ingredients and recipes. In particular, these notions lead to the establishment of some bounds on the number and distribution of 2-coboundaries over Zt x Z2,2 to use and the way in which they have to be combined in order to obtain a Zt x Z2,2-cocyclic Hadamard matrix. Exhaustive searches have been performed, so that the table in p. 132 in [BH95] is corrected and completed. A deeper look at the results obtained leads to the definition of some transformations which preserve the Zt x Z2,2-cocyclic Hadamard character of a matrix, and which give rise to orbits of Zt x Z2,2-cocyclic Hadamard matrices. This will be explained in a subsequent paper [AGG11], due to space limitations.

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