Weight Enumerator Theorems

Abstract

In the past few years, a large number of results have appeared in the literature concerning the distribution of weights in various codes. Explicit formulas are now known for the number of codewords of each weight in several infinite classes of codes. As mentioned earlier in this paper, these results allow one to compute the probability of decoding failure and the probability of decoding error when one of these codes is decoded by a t-error-correcting decoding algo — rithm, where t may be any number less than half of the code’s minimum distance.