Perfect and Quasi-Perfect Codes Under the $l_{p}$ Metric
Tao Zhang, Gennian Ge · IEEE Transactions on Information Theory · 2017
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 ≥ 3 and r > 1. In this paper, we study perfect codes in Zn under the l p metric, where 11/p, 31/p. We also give an algebraic construction of quasi-perfect lpcodes for p = 1, r = 2, and 2 <; p <; ∞, r = 21/p.