2019/04/25 by Santiago Barrera Acevedo, Acevedo, Santiago Barrera, Heiko Dietrich +3
Mathematics · #05B10 #05B20 #20J06 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #math.CO #math.GR #msc:05B10 #msc:05B20 #msc:20J06
paper · pdf · doi:10.48550/arxiv.1904.11460
12 pages, 2 tables
arxiv created 2019/07/17 · arxiv updated 2019/07/18
Cocyclic Hadamard matrices (CHMs) were introduced by de Launey and Horadam as a class of Hadamard matrices 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. Based on 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 \leqslant 13. Our analysis shows that every CHM of order 4p with p≡ 1\bmod 4 is equivalent to a Hadamard matrix with one of five distinct block structures, including Williamson type and (transposed) Ito matrices. If p≡ 3 \bmod 4, then every CHM of order 4p is equivalent to a Williamson type or (transposed) Ito matrix.