Error-Correcting Codes and Minkowski’s Conjecture

Authors

Peter Horak, University of Washington TacomaFollow

Publication Date

12-1-2010

Document Type

Article

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.

Publication Title

Tatra Mountains Mathematical Publications

Volume

45

Issue

1

First Page

37

Last Page

49

DOI

10.2478/v10127-010-0004-y

Open Access Status

OA Deposit

Comments

This article was originally published in Tatra Mountains Mathematical Publications. The final publication is available at www.degruyter.com.