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Title: Non-existence of perfect 2-error correcting Lee codes of word length 7 over Z
Author: Cruz, Catarina
Breda, Ana
Keywords: Perfect Lee codes
Golomb-Welch conjecture
Lee metric
Issue Date: Nov-2018
Publisher: World Academy of Science, Engineering and Technology
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.
Peer review: yes
Publisher Version:,--2018,-20-(11)-Part-II.pdf
Appears in Collections:CIDMA - Comunicações

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