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