Efficient bounded-distance decoding of the hexacode and associated decoders for the Leech lattice and the Golay code

Abstmct Two soft-decision algorithms f o r decoding the (6,3,4) q u a t e r n a r y code, the hezocode, are p resented. Both algorithms have the same guaranteed error cor rec t ion radius as that of maximum-likelihood decoding. In using them, bounded-distance decoding of the Golay code and the Leech lattice are performed i n at most 187 and 519 real operations respectively. We present s o m e s imula t ion results for the Leech lattice decoder revea l ing near -opt imal performance. A compar ison to k n o w n trellis codes is also provided.