Geodesic
Strongly orthogonal and uniformly orthogonal many-placed operations
Algebra and discrete mathematics, no. 1 (2006), pp. 1-17

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In [3] we have studied connection between orthogonal hypercubes and many-placed ($d$-ary) operations, have considered different types of orthogonality and their relationships. In this article we continue study of orthogonality of many-placed operations, considering special types of orthogonality such as strongly orthogonality and uniformly orthogonality. We introduce distinct types of strongly orthogonal sets and of uniformly orthogonal sets of $d$-ary operations, consider their properties and establish connections between them.
Keywords: $d$-ary operation, $d$-ary quasigroup, orthogonal $d$-ary operations, strongly orthogonal operations, uniformly orthogonal operations.
Mots-clés : hypercube, orthogonal hypercubes 
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G. Belyavskaya; Gary L. Mullen. Strongly orthogonal and uniformly orthogonal many-placed operations. Algebra and discrete mathematics, no. 1 (2006), pp. 1-17. http://geodesic.mathdoc.fr/item/ADM_2006_1_a0/