Restriction conditions on PL(7, 2) codes (3 ≤ |𝓖i| ≤ 7)

Restriction conditions on PL(7, 2) codes (3 ≤ |𝓖i| ≤ 7) AbstractThe 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Open Mathematics de Gruyter

Restriction conditions on PL(7, 2) codes (3 ≤ |𝓖i| ≤ 7)

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Publisher
De Gruyter
Copyright
© 2018 Cruz and ďAzevedo Breda, published by De Gruyter
ISSN
2391-5455
eISSN
2391-5455
D.O.I.
10.1515/math-2018-0027
Publisher site
See Article on Publisher Site

Abstract

AbstractThe 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.

Journal

Open Mathematicsde Gruyter

Published: Apr 2, 2018

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