2011/12/19 by Victor Alvarez, Víctor Álvarez, Alvarez, Victor +6
Engineering · Mathematics · #05B20 #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #graph theory and CDMA systems #math.CO #msc:05B20
paper · pdf · doi:10.48550/arxiv.1112.4296
19 pages (main paper) + 7 pages (Appendix); it is the result of merging arXiv:1112.4296 [math.CO] and arXiv:1112.4300 [math.CO] papers
openalex publication_date 2011/12/19 · arxiv created 2014/06/10 · arxiv updated 2014/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A characterization of ℤ t × ℤ22-cocyclic Hadamard matrices is described, depending on the notions of \em distributions, \em ingredients and \em recipes. In particular, these notions lead to the establishment of some bounds on the number and distribution of 2-coboundaries over ℤt × ℤ 22 to use and the way in which they have to be combined in order to obtain a ℤ t × ℤ22-cocyclic Hadamard matrix. Exhaustive searches have been performed, so that the table in p. 132 in [4] is corrected and completed. Furthermore, we identify four different operations on the set of coboundaries defining ℤ t × ℤ22-cocyclic matrices, which preserve orthogonality. 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, in terms of \em diagrams. Let \cal H be the set of cocyclic Hadamard matrices over ℤt × ℤ22 having a symmetric diagram. We also prove that the set of Williamson type matrices is a subset of \cal H of size \frac|\cal H|t.