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Hadamard matrices of generalized quaternion type. (English) Zbl 0725.05028
The work is devoted to the problem of Hadamard matrix (H.M.) construction using the group-theoretical approach. H.M. is determined as a right regular representation of matrix of an element in R, which is obtained from the group ring ZG, where G is a semi-direct product of a cyclic group of an odd order by a generalized quaternion group $$Q_ s$$. In particular, if $$s=1$$, the considered H.M. are H.M. of type Q, and adding the condition that the submatrices of H.M. of type Q are symmetric, they become H.M. of Williamson type.
In the paper the existence of some infinite series of H.M. of generalized quaternion type using the theory of the relative Gauss sum, is given.

##### MSC:
 05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)