On bounds, tags and speeds

[David Lucas]

While working on punctured codes, the following question(s) arose:

When several bounds are available to compute the same thing, which one should we choose? And/or what behaviour should we always have when it comes to this kind of choices?

Concrete example:

On punctured codes, the minimum distance computation is not straightforward. Especially if one punctures a cyclic code, which has several bounds on the minimum distance. In that case, which bound should be used to compute punctured code's minimum distance?

I was considering the idea of introducing some kind of "tags" (or labels) system to bounds, as we did with decoders. In that case, the choice of a bound could be automatized thanks to these tags. But, for now, bounds are only class methods (e.g. BCH_bound is a class method in cyclic codes), and this kind of labelling thing could lead us to another object structure...

So, do you have any thoughts on this problem?

[Daniel Augot]

I think the answer is mathematical : one wants the best bound (upper or lower). So as long as there is no combinatorial explosion, all the bounds should computed and may be combined.

[David Lucas]

See issue #150.