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- Title
Constructing cocyclic Hadamard matrices of order 4p.
- Authors
Barrera Acevedo, Santiago; Ó Catháin, Padraig; Dietrich, Heiko
- Abstract
Cocyclic Hadamard matrices (CHMs) were introduced by de Launey and Horadam as a class of Hadamard matrices (HMs) with interesting algebraic properties. Ó Catháin and Röder described a classification algorithm for CHMs of order 4n based on relative difference sets in groups of order 8n; this led to the classification of all CHMs of order at most 36. On the basis of work of de Launey and Flannery, we describe a classification algorithm for CHMs of order 4p with p a prime; we prove refined structure results and provide a classification for p≤13. Our analysis shows that every CHM of order 4p with p≡1 mod4 is equivalent to a HM with one of five distinct block structures, including Williamson‐type and (transposed) Ito matrices. If p≡3 mod4, then every CHM of order 4p is equivalent to a Williamson‐type or (transposed) Ito matrix.
- Subjects
HADAMARD matrices; DIFFERENCE sets; ORDERED sets; CLASSIFICATION algorithms
- Publication
Journal of Combinatorial Designs, 2019, Vol 27, Issue 11, p627
- ISSN
1063-8539
- Publication type
Article
- DOI
10.1002/jcd.21664