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• W2600787501 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 $ngeq 3$ and $r>1$ . In this paper, we study perfect codes in $mathbb {Z}^{n}$ under the $l_{p}$ metric, where $1leq p . We show some nonexistence results of linear perfect $l_{p}$ codes for $p=1$ and $2leq p , $r=2^{1/p},3^{1/p}$ . We also give an algebraic construction of quasi-perfect $l_{p}$ codes for $p=1, r=2$ , and $2leq p ." @default.
• W2600787501 created "2017-04-07" @default.
• W2600787501 creator A5029449317 @default.
• W2600787501 creator A5052545361 @default.
• W2600787501 date "2017-07-01" @default.
• W2600787501 modified "2023-10-17" @default.
• W2600787501 title "Perfect and Quasi-Perfect Codes Under the $l_{p}$ Metric" @default.
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• W2600787501 doi "https://doi.org/10.1109/tit.2017.2685424" @default.
• W2600787501 hasPublicationYear "2017" @default.
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