Two kinds of algorithms are considered. 1) 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). 2) Similarly, a decoding algorithm for a lattice \Lambda in R^{n} changes an arbitrary point of R^{n} into a closest lattice point. Some general methods are given for constructing such algorithms, ami are used to obtain new and faster decoding algorithms for the Gosset lattice E_{8} , the Golay code the Leech lattice.

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Soft decoding techniques for codes and lattices, including the Golay code and the Leech lattice

We introduce exceptionally simple decoding algorithms for the two extended Golay codes The algorithms are based on recent methods of Conway and Curtis of finding the unique blocks containing five points in either the (5,8,24) Steiner system or the (5,6,12) Steiner system These decoding methods are simple enough to enable decoding extended Golay codes by hand Both of the methods involve relations between the extended Golay codes and other self-dual codes Proofs are given explaining these relationships and why the decoding methods work The decoding algorithms are explained and illustrated with many examples [3 , chap 12] has facts about the Mathieu group and some details about decoding the Golay codes

Decoding the Golay codes

Information sets and partial permutation decoding for codes from finite geometries

By finding explicit PD-sets we show that permutation decoding can be used for the binary code obtained from an adjacency matrix of the triangular graph T(n) for any n ≥ 5.

/pdf/permutation-decoding-for-the-binary-codes-from-triangular-3qjsqmd52v.pdf

Permutation decoding for the binary codes from triangular graphs

We give a minimal set consisting of 14 permutations to decode the (24,12,8) Golay code using a permutation decoding method.

A permutation decoding of the (24, 12, 8) Golay code (Corresp.)

For permutation decoding of an e error-correcting linear code, a set of permutations which move all error vectors of weight \leq e out of the information places is needed. A method of finding minimal decoding sets is given, along with minimal sets obtained with this method for the binary Golay codes.

D. Gordon

Papers

Minimal permutation sets for decoding the binary Golay codes (Corresp.)