Practical considerations

In practice, computing the $\mathfrak{G}$-construction using Algorithm  is only feasible for high-rate codes because the algorithm needs to maintain a list of coset leaders at each iteration.

Another problem with the $\mathfrak{G}$-construction is that it is theoretically possible for bounding to be so severe as to halt the construction when, for example, $f(\ensuremath{{\mathbb{C}}})$ does not return a vector for a particular code $\mathbb {C}$. Though we have not seen this with trellis state bounding (i.e., using the mapping $\ensuremath{f_{\mbox{\small state}}}$), we have seen indications that this can occur with $\ensuremath{f_{\mbox{\small decoding}}}$. Of course, certain constraints will simply not correspond to any existing linear code, so this problem is inherent to code design.