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Title: Restriction conditions on PL(7, 2) codes (3 ≤ |𝓖_i| ≤ 7)
Author: Cruz, Catarina N.
Breda, Ana
Keywords: Perfect Lee codes
Golomb-Welch conjecture
Space tilings
Issue Date: 2-Apr-2018
Publisher: De Gruyter
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 mathematics and computer sciences. Many results on this subject have been achieved, however the conjecture is only solved for some particular values of n and r, namely: 3 ≤ n ≤ 5 and r ≥ 2; n = 6 and r = 2. Here we give an important contribution for the case n = 7 and r = 2, establishing cardinality restrictions on codeword sets.
Peer review: yes
DOI: 10.1515/math-2018-0027
ISSN: 2391-5455
Appears in Collections:CIDMA - Artigos
AGG - Artigos

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