Elsevier

Discrete Mathematics

Volume 309, Issue 18, 28 September 2009, Pages 5551-5561
Discrete Mathematics

On perfect Lee codes

Dedicated to the occasion of the 60-th birthday of Pavol Hell
https://doi.org/10.1016/j.disc.2008.03.019Get rights and content
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Abstract

In this paper we survey recent results on the Golomb–Welch conjecture and its generalizations and variations. We also show that there are no perfect 2-error correcting Lee codes of block length 5 and 6 over Z. This provides additional support for the Golomb Welch conjecture as it settles the two smallest cases open so far.

Keywords

Perfect Lee code
Golomb–Welch conjecture

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