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On the multiplication theorems of Hadamard matrices of generalized quaternion type using $$M$$-structures. (English) Zbl 0784.05017
This paper may be said to be a sequel to a paper by the second author [Hadamard matrices of generalized quaternion type, Discrete Math. 87, No. 2, 187-196 (1991; Zbl 0725.05028)]. First the authors describe $$M$$- structure Hadamard matrices $$H$$ of order $$4n$$ and of generalized quaternion type. The main results of the authors state two constructions of $$M$$-structure Hadamard matrices of order $$4nm$$ based on $$H$$ and a quartet or a pair of $$\{-1,0,1\}$$-matrices of order $$m$$ satisfying several conditions. The definitions and results are a little too complicated to be reproduced here explicitly.
##### MSC:
 05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)