Constrained designs for maximum likelihood soft decoding of RM(2,m) and the extended Golay codes

We present algorithms for maximum likelihood soft decoding of the second order Reed-Muller codes RM(2,m) and the extended (24,12,8) Golay code. The decoding procedures are based on a concise representation of appropriately selected cosets of a subcode of the code considered. Such representation enables application of certain elimination rules. A structure, called constrained design, is established to support the elimination procedures. Remarkably efficient algorithms are obtainable by this approach. The method of elimination is applicable also in combination with existing coset decoding schemes.<>