Perfect codes in the Lee metric

Meeting Time: March 2, 2010, 2:00-2:50pm

Abstract: The Lee distance between two n-dimensional points with entries in the integers modulo m is the sum of the least absolute difference between the components. This is a metric (which happens to agree with the Hamming metric for m=2 and m=3), so it is natural to investigate the existence of perfect codes over this metric. In 1970, Golomb and Welch showed that Lee balls of radius r tile n-dimensional space when n=1 or 2, in which case Lee balls of any radius will pack, while r=1 gives a packing for any n. It is conjectured that these are the only cases that such a tiling exists. In this talk we will look at the paper in which these results appeared, as well as considering more recent direction in the quest to prove the non-existence of packings in the other cases.