A note on the computation of the bit error rate for binary block codes

AbstractThe bit error rate of binary codes on the binary symmetric channel with raw error probability p is a performance index of primary importance in many applications. It is the probability that decoded information symbols are in error after complete decoding. In this paper the class of linear block codes having a transitive group of automorphisms is considered. It is shown that a linear homogeneous differential transformation of the weight enumerator enables us to obtain a closed expression for the bit error rate in terms of p. The application of the method is general enough to allow the computation of bit error rates for all cyclic codes