On autotopies and automorphisms of $n$-ary linear quasigroups

In this article we study structure of autotopies, automorphisms, autotopy groups and automorphism groups of $n$-ary linear quasigroups.
We find a connection between automorphism groups of some special kinds of $n$-ary quasigroups (idempotent quasigroups, loops) and some isotopes of these quasigroups. In binary case we find more detailed connections between automorphism group of a loop and automorphism group of some its isotope. We prove that every finite medial $n$-ary quasigroup of order greater than 2 has a non-identity automorphism group.
We apply obtained results to give some information on automorphism groups of $n$-ary quasigroups that correspond to the ISSN code, the EAN code and the UPC code.