Title:  Codes in Lee metric and the Golomb-Welch Conjecture

Abstract: Lee metric was introduced by Lee and Ulrich for transmission of signals taken from GF(p) over noisy channels. The interest in Lee codes is due to many applications of them. For example, constrained and partial-response channels, flash memory, interleaving schemes, placement of resources in the computer architecture that minimizes access time by processing elements etc. Golomb and Welch raised a conjecture 50 years ago concerning the existence of perfect e-error-correcting codes in the Lee metric. This conjecture lies at the very center of interests in the area of perfect codes in the Lee metric. In spite of great effort and plenty of papers on the topic, the Golomb-Welch conjecture is still far from being solved. In our talk we will survey results on this conjecture and discuss the latest development.