Hellooooooooo !

> There is no significantly faster method than trying all possibilities.
> Finding the minimum-weight codewords of a linear code is a hard problem.
> Since your code is not too big, the naive method takes only a few seconds.

Thanks for your answer. As it takes something like 40s and that it is
meant to become a Sage function, I hardcoded the result as compacty as
possible. We will have two versions of that code, the hardcoded one
(default) and the one that builds it from scratch (very long..) if we
need to check, or if the running time ever improves.

The ticket is http://trac.sagemath.org/ticket/19180.

> There are clever algorithms (still exponential) for computing the weight of
> the minimal weight codewords (the minimum distance of the code). I'm unaware
> whether these might be (or have been) modified to provide all minimum weight
> codewords, which could result in a practically significant speedup over the
> naive method.

HMmm... The odd thing is that %prun does not say much about what the
bottleneck is in those computations. It seems that GAP works in the
background, but I do not see it there ...

Nathann

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