Construction of medial ternary self-orthogonal quasigroupsm

Abstract

Algorithms for checking if a medial ternary quasigroup has a set of six triple-wise orthogonal principal parastrophes and a set of six triple-wise strongly orthogonal principal parastrophes are found. It is proved that $n$-ary strongly self-orthogonal linear (including medial) quasigroups do not exist when $n>3$.