Nonexistence of perfect 2-error-correcting Lee codes in certain dimensions

The Golomb-Welch conjecture states that there are no perfect e-error-correcting codes in Zn for n≥3 and e≥2. In this note, we prove the nonexistence of perfect 2-error-correcting codes for a certain class of n, which is expected to be infinite. This result further substantiates the Golomb-Welch conjecture.