This paper considers two kinds of algorithms. (i) If # is a binary code of length n, a "soft decision " decoding algorithm for # changes an arbitrary point of R n into a nearest codeword (nearest in Euclidean distance). (ii) Similarly a decoding algorithm for a lattice L in R n changes an arbitrary point of R n into a closest lattice point. Some general methods are given for constructing such algorithms, and are used to obtain new and faster decoding algorithms for the Gosset lattice E 8, the Golay code and the Leech lattice.
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