Fast decoding of quasi-perfect Lee distance codes

A code D over Z2n is called a quasi-perfect Lee distance-(2t + 1) code if dL(V,W) ≥ 2t + 1 for every two code words V,W in D, and every word in Z2n is at distance  ≤  t + 1 from at least one code word, where DL(V,W) is the Lee distance of V and W. In this paper we present a fast decoding algorithm for quasi-perfect Lee codes. The basic idea of the algorithm comes from a geometric representation of D in the 2-dimensional plane. It turns out that to decode a word it suffices to calculate its distance to at most four code words.