PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 29(43), pp. 5359 (1981) 

ON FINITE MULTIQUASIGROUPSGeorgi Cupona, Zoran Stojakovi\'c and Janez UsanPrirodnomatematicki fakultet, Skopje, Macedonia and Institut za matematiku, Novi Sad, YugoslaviaAbstract: 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 $m\leq q1$, 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. Full text of the article:
Electronic fulltext finalized on: 3 Nov 2001. This page was last modified: 16 Nov 2001.
© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
