Error-correcting codes and Minkowski's conjecturre

Abstract

The goal of this paper is twofold. The main one is to survey the
latest results on the perfect and quasi-perfect Lee error correcting codes. The
other goal is to show that the area of Lee error correcting codes, like many ideas
in mathematics, can trace its roots to the Phytagorean theorem a2+b2 = c2. Thus
to show that the area of the perfect Lee error correcting codes is an integral part
of mathematics. It turns out that Minkowski’s conjecture, which is an interface of
number theory, approximation theory, geometry, linear algebra, and group theory
is one of the milestones on the route to Lee codes.