Abstract
AbstractCocyclic 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 based on relative difference sets in groups of order ; 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 with a prime; we prove refined structure results and provide a classification for . Our analysis shows that every CHM of order with is equivalent to a HM with one of five distinct block structures, including Williamson‐type and (transposed) Ito matrices. If , then every CHM of order is equivalent to a Williamson‐type or (transposed) Ito matrix.
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