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On a family of cocyclic Hadamard matrices. (English) Zbl 1029.05025
Arasu, K. T. (ed.) et al., Codes and designs. Proceedings of a conference honoring Professor Dijen K. Ray-Chaudhuri on the occasion of his 65th birthday, The Ohio State University, Columbus, OH, USA, May 18-21, 2000. Berlin: de Gruyter. Ohio State Univ. Math. Res. Inst. Publ. 10, 187-205 (2002).
The paper describes the construction of a large family of cocyclic Hadamard matrices based on relative difference sets with central forbidden subgroup of size two. In particular, it is proved that any group of odd square-free order $$p_1p_2\cdots p_n$$ (where $$p_i$$ is prime) can be embedded in a group of order $$2^{n+1}(p_1+ 1)(p_2+ 1)\cdots(p_n+1) p_1p_2\cdots p_n$$ that contains such a relative difference set.
For the entire collection see [Zbl 0996.00030].

##### MSC:
 05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.) 05B10 Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.)
##### Keywords:
relative difference sets