Non-Existence of Linear Perfect Lee Codes With Radius 2 for Infinitely Many Dimensions
Claudio Qureshi, Antonio C. de A. Campello, Sueli I. R. Costa · IEEE Transactions on Information Theory · 2018
The Golomb-Welch conjecture (1968) on the non-existence of perfect Lee codes in Znwith radius e ≥ 2 and dimensions n ≥ 3, widely believed to be true, has been up to now only proved for large radius in any dimension, for small dimensions, and for some small radii and specific n. The main result of this paper is that for radius e = 2, there are no perfect Lee linear codes in Znfor infinitely many values of n.