PART C - DISCUSSION OF RESULTS The probability of decoding error varies quite a bit from one random number seed to another, especially for small channel error probabilities, where the decoding error can vary by more than a factor of two. For a given rate, larger codes tend to be better, but due to variability with random number seed, this is not true in every case. The rate 0.5 codes have lower decoder error probability than the rate 0.6 codes, for a given channel error probability. For example, if we require that the decoder error probability be less than 0.1, the highest noise probability we could tolerage when using one of the rate 0.6 codes is 0.04, whereas when using one of the rate 0.5 codes, we could achieve that low a decoder error probability when the channel error probability is 0.06. Note that neither result is close to the limit based on channel capacity, since the capacity s 0.6 when the channel error probability is 0.08, and 0.5 when the channel error probability is 0.11. Larger block sizes are needed to approach the channel capacity with small decoding error probability. However, the decoding error probability is much less than the probability of at least one message bit being incorrect if they are sent unencoded. For example, the [25,10] code has 15 message bits, which would be received with at least one error with probability 0.14 at channel error probability 0.01. This message error probability is ten times the decoder error probability of the worst of the [25,10] codes. There are some pairs of codes for which one is better at low channel error probability whereas the other is better at high channel error probability. For example, pchk-14-28-1 is better than pchk-14-28-2 for channel error probability 0.01, but worse for channel error probability 0.15. This can be explained by looking at the histograms for the weights of correctable error patterns. The 14-28-1 code corrects more error patterns of weight 2, which will be important for low channel error probability. However, it corrects fewer error patterns of weight 4. Since the expected number of errors when the channel error probability is 0.15 is 4.2, the better correction of weight 4 error patterns by the 14-28-2 code gives it better performance at that noise level.