The performance of optimum linear block codes has been examined by computer simluation, and the error distribution at the decoder output, the block-error probability and the bit-error probability have been determined for the codes when they are used on a binary symmetric channel with random errors. A table showing the distribution of errors in the decoder output is presented, and it is shown how the table can be used to determine exact values for the bit-error probability and the block-error probability. The exact values of bit-error probability computed from the table are compared with values obtained using a known theoretical approximation to the bit-error probability, and some conclusions are drawn as to the general usefulness of the theoretical approximation. Also, block-error probabilities are computed from the information presented in the table and these values are compared with the estimates of block-error probability obtained from minimumdistance considerations.