A decoding rule is presented which minimizes the probability of symbol error over a time-discrete memoryless channel for any linear error-correcting code when the code words are equiprobable. The complexity of this rule varies inversely with code rate, making the technique particularly attractive to high rate codes. Examples are given for both block and convolutional codes.
Hartmann, Carlos R.P. and Rudolph, Luther D., "An Optimum Symbol-by Symbol decoding rule for linear codes" (1975). Electrical Engineering and Computer Science Technical Reports. 8.