Weight enumerators of high-rate convolutional codes based on the Hamming code (Q1177492)

The author considers a class of rate \((n-1)/n\;(n=2^ r,\;r=1,2,\dots)\) binary convolutional codes with free distance \(d_ f=3\) and derives a method for the calculation of their spectra. Moreover she shows that the codes of this class are equivalent to punctured convolutional codes having constraint length \(\leq r+1\) and allow maximum likelihood decoding with complexity of order \(2^{r+1}\).