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Some results on orthogonal designs and Hadamard matrices. (English) Zbl 1099.05016

Summary: Amicable sets of matrices are widely used in the construction of orthogonal designs for orders divisible by eight. In this paper we use a general construction method for up to eight variables orthogonal designs of order \(8n\) to construct two new full orthogonal designs. Using this method and the new derived designs, a number of inequivalent Hadamard matrices and skew-Hadamard matrices are obtained.

MSC:

05B15 Orthogonal arrays, Latin squares, Room squares
05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
62K10 Statistical block designs
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