On ZZt × ZZ2 2-cocyclic Hadamard matrices
|Author/s||Álvarez Solano, Víctor
Gudiel Rodríguez, Félix
Güemes Alzaga, María Belén
|Department||Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Universidad de Sevilla. Departamento de álgebra
|Abstract||A characterization of ZZt × ZZ22
-cocyclic Hadamard matrices is described, de-
pending on the notions of distributions, ingredients and recipes. In particular,
these notions lead to the establishment of some bounds on ...
A characterization of ZZt × ZZ22 -cocyclic Hadamard matrices is described, de- pending 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 ZZt × ZZ22 to use and the way in which they have to be combined in order to obtain a ZZt × ZZ22 -cocyclic Hadamard matrix. Exhaustive searches have been performed, so that the table in p. 132 in  is corrected and completed. Furthermore, we identify four different operations on the set of coboundaries defining ZZt × ZZ22 -cocyclic matrices, which preserve orthogonality. We split the set of Hadamard matrices into disjoint orbits, de- fine representatives for them and take advantage of this fact to compute them in an easier way than the usual purely exhaustive way, in terms of diagrams. Let H be the set of cocyclic Hadamard matrices over ZZt × ZZ22 having a sym- metric diagram. We also prove that the set of Williamson type matrices is a subset of H of size |H| t .
|Citation||Álvarez Solano, V., Gudiel Rodríguez, F. y Güemes Alzaga, M.B. (2015). On ZZt × ZZ2 2-cocyclic Hadamard matrices. Journal of Combinatorial Designs, 23 (8), 352-368.|