On minimum Lee distances of generalized Reed-Muller codes

The authors give a lower bound for the minimum Lee distance of a GRM code with code length p^m-1 (p:prime) in terms of the minimum Lee distances of a GRM code of code length p -1 and an extended GRM code of code length p. They also give the true minimum Lee distances for special classes of GRM codes. Since the true minimum distances of GRM and extended GRM codes with shorter code length can be obtained rather easily by computer search, the expression for a lower bound derived enables them to get a lower bound of the minimum Lee distance of a GRM code having a longer code length. They also show through numerical examples that there are many GRM codes whose minimum Lee distances really exceed minimum Hamming distances, which implies that they may be effectively used as error control codes in systems employing multilevel signaling