Non-existence of perfect 2-error correcting Lee codes of word length 7 over Z

Abstract

The Golomb-Welch conjecture states that there is no perfect r-error correcting Lee code of word length n over Z for n≥3 and r≥2. This problem has received great attention due to its importance in applications in several areas beyond mathematicsand computer sciences. Here, we give a contribution for the proof of the Golomb-Welch conjecture which reinforces it, proving the non-existence of perfect 2-error correcting Lee codes of word length 7 over Z.