Weight Enumerators of High-Rate Convolutional Codes Based on the Hamming Code

We derive an analytical expression for the weight enumerator of a class of convolutional codes with rate $R=(n-1)/n$, $n=2^r$, $r=1,2,\dots$, and free distance $d_f=3$. We show that the codes of this class are equivalent to punctured convolutional codes with constraint length $\leq{r+1}$ and admit decoding with complexity of order $\leq 2^{r+1}$.