ON FINITE MULTIQUASIGROUPS

Georgi Cupona, Zoran Stojakovi\'c and Janez Usan

Abstract: In the present paper multiquasigroups and their relations to orthogonal systems of operations and codes are studied. In the first part of the paper the notion of an $[n,m]$-quasigroup of order $q$ is defined and it is shown that for $n,m,q\geq 2$ it follows that $m\leq q-1$, in the second part, as a corollary of the preceding result, an upper bound for the maximal number of $n$-ary operations in an orthogonal system of operations on a set with $q$ elements is obtained. In the third part the existence of a class of multiquasigroups is shown, and in the fourth part a connection between multiquasigroups and a special kind of code is pointed out.

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