<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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 <italic>a</italic>2+<italic>b</italic>2 = <italic>c</italic>2. 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.</p></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.

Error-correcting codes and Minkowski’s conjecture

IAS University of Washington, Tacoma, WA 98402–3100, U.S.A

Tatra Mountains Mathematical Publications

{"article-title":"Error-correcting codes and Minkowski\u2019s conjecture"}

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...

Error-correcting codes and Minkowski’s conjecture

Published Online: Nov 12, 2012

Page range: 37 - 49

DOI: https://doi.org/10.2478/v10127-010-0004-y

Keywords
Lee codes, tilings, unit cubes.

This content is open access.

Error-correcting codes and Minkowski’s conjecture

Published Online: Nov 12, 2012

Page range: 37 - 49

DOI: https://doi.org/10.2478/v10127-010-0004-y

KeywordsLee codes, tilings, unit cubes.

This content is open access.

Keywords
Lee codes, tilings, unit cubes.