1. Perfect and Quasi-Perfect Codes Under the lp Metric.
- Author
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Zhang, Tao and Ge, Gennian
- Subjects
- *
PERFECT codes , *SIGNAL processing , *TILING (Mathematics) , *ERROR correction (Information theory) , *DECODING algorithms - 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]
- Published
- 2017
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