Publications de l’Institut Mathématique, Nouvelle Série, Vol. 101[115], pp. 109

Publications de l’Institut Mathématique, Nouvelle Série
Vol. 101[115], pp. 109–119 (2017)

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ON CONSTRUCTION OF ORTHOGONAL $d$ -ARY OPERATIONS

Smile Markovski, Aleksandra Mileva

Faculty for Computer Science and Engineering, Ss Cyril and Methodius University, Skopje, Macedonia; Faculty for Infromatics, Goce Delcev University, Stip, Macedonia

Abstract: A $d$ -hypercube of order $n$ is an ${\underset{︸}{n \times \dots \times n}}_{d}$ array with $n^{d}$ elements from a set $Q$ of cardinality $n$ . We recall several connections between $d$ -hypercubes of order $n$ and $d$ -ary operations of order $n$ . We give constructions of orthogonal $d$ -ary operations that generalize a result of Belyavskaya and Mullen. Our main result is a general construction of $d$ -orthogonal $d$ -ary operations from $d$ -ary quasigroups.

Keywords: Latin hypercube; orthogonal hypercubes; orthogonal functions; recursively differentiable quasigroups

Classification (MSC2000): 05B15; 20N05; 20N15

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Electronic fulltext finalized on: 24 Apr 2017. This page was last modified: 11 May 2017.

© 2017 Mathematical Institute of the Serbian Academy of Science and Arts
© 2017 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition

ON CONSTRUCTION OF ORTHOGONAL d-ARY OPERATIONS

Smile Markovski, Aleksandra Mileva

ON CONSTRUCTION OF ORTHOGONAL $d$ -ARY OPERATIONS