On Finite Multiquasigroups

Georgi Čupona ; Zoran Stojaković ; Janez Ušan

Publications de l'Institut Mathématique, _N_S_29 (1981) no. 43, p. 53

Résumé

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.