Abstract: In this paper, Bruck and Blaum's conclusions are generalized in two aspects. On the one band, the maximum likelihood decoding of linear block codes in the soft-decision condition is proved to be equivalent to making a neural network converge to a globe stable state of the energy function. On the other hand, we construct such an associative memory neural network for a linear block code in GF(p) that each codeword of the code is respctive to a globe maximum point of the energy function of the neural network.

Key words: information theory, digital communication, error-correcting code, maximum likelihood decoding, neural network, associative memory