Even more efficient bounded-distance decoding of the hexacode, the Golay code, and the Leech lattice

摘要

We present a new bounded-distance decoding algorithm for the hexacode, which requires at most 34 real operations in the worst case, as compared to 57 such operations in the best previously known decoder. The new algorithm is then employed for bounded-distance decoding of the Leech lattice and the Golay code. The error-correction radius of the resulting decoders is equal to that of a maximum-likelihood decoder. The resulting decoding complexity is at most 331 real operations for the Leech lattice and at most 121 operations for the Golay code. For all the three codes-the hexacode, the Golay code, and the Leech lattice-the proposed decoders are considerably more efficient than any decoder presently known.