Override sanity checks on decoder's output

[David Lucas]

Since we added sanity checks on the output of decode_to_code and decode_to_message, some decoding algorithms now need to compute the parity check matrix to be performed.

Forcing this behaviour is quite a shame for decoding algorithms which don't need the generator matrix nor the parity check matrix to run.

I propose to add a flag checks = True which ignore all sanity checks if set to False.

What do you think?

[Johan Rosenkilde]

I disagree. I very highly doubt there is any algorithm for decoding any code which in its working is not powerful enough to determine whether a vector is a codeword or not.

Rather, it might be the case that the default implementation c in C, which computes the parity check matrix (and therefore usually also the generator matrix) might be inefficient for certain codes. There should therefore always be a way to formulate your decoder such that it is not (asymptotically) slower, but such that the generator/parity check matrices need not be computed.

Take GRS codes as our canonical example. The Gao decoder begins by computing a Lagrange polynomial of the received word. This computation itself determines whether the received word is in the code: indeed, if deg R < k then r in C. I've mentioned this several times before. If you want to patch decoding of GRS codes, patch that.