1. A method for decoding a received vector of corrupted symbols encoded using a code set comprised of a plurality of code words, said method comprising the steps of: representing said received vector of corrupted symbols as a vector having group algebra elements; multiplying said vector having group algebra elements by a first matrix associated with said code set to obtain conditional probabilities for all code words; multiplying said conditional probabilities by a second matrix associated with said code set to obtain a vector of values indicating a probability for each possible value for each symbol; and selecting a value having a maximum probability of said indicated probabilities for each possible value for each symbol.