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Cocyclic Hadamard matrices and difference sets. (English) Zbl 0956.05026
The authors explain the connection between (relative) difference sets, cocyclic Hadamard matrices, cocycles, coboundaries and perfect binary arrays. In particular, they mention the interesting conjecture that for any \(t\), cocyclic Hadamard matrices of order \(4t\) exist. The authors show that many of the known families of Hadamard matrices are actually families of cocyclic Hadamard matrices.

MSC:
05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
05B10 Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.)
20J06 Cohomology of groups
05B05 Combinatorial aspects of block designs
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