Some new operations on Zt x Z2,2-cocyclic Hadamard matrices

Details Some new operations on Zt x Z2,2-cocyclic Hadamard matrices Some new operations on Zt x Z2,2-cocyclic Hadamard matrices

2011-12-19

arxiv.org/abs/1112.4300v1

Mathematics

Combinatorics

17 pages

Scientific paper

Following the ideas of [AGG11] about Zt x Z2,2-cocyclic Hadamard matrices, we introduce the notion of diagram, which visually represents any set of coboundaries. Diagrams are a very useful tool for the description and the study of paths and intersections, as described in [AGG11]. Then, we will study four different operations on Zt x Z2,2-cocyclic matrices. These operations will be defined on the set of coboundaries defining the matrix, preserve the Hadamard character of the cocyclic matrices, and allow us to obtain new Hadamard matrices from old ones. We split the set of Hadamard matrices into disjoint orbits, define representatives for them and take advantage of this fact to compute them in an easier way than the usual purely exhaustive way.

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