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

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