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Perfect and Quasi-Perfect Codes Under the lp Metric.
- Source :
-
IEEE Transactions on Information Theory . Jul2017, Vol. 63 Issue 7, p4325-4331. 7p. - Publication Year :
- 2017
-
Abstract
- A long-standing conjecture of Golomb and Welch, raised in 1970, states that there is no perfect r error correcting Lee code of length n for n\geq 3 and r>1 under the l_{p} metric, where 1\leq p<\infty . We show some nonexistence results of linear perfect lp codes for p=1 and 2\leq p<\infty , r=2^{1/p},3^{1/p} . We also give an algebraic construction of quasi-perfect l_{p}$ codes for p=1, r=2$ , and 2\leq p<\infty , r=2^{1/p} . [ABSTRACT FROM PUBLISHER]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 63
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 123685216
- Full Text :
- https://doi.org/10.1109/TIT.2017.2685424