As part of the evaluation for GSoC project I present the results obtained so far.
I have implemented a new decoding algorithm GDDA (gradient descent decoding algorithm) based on the grobner representation of a code.
The idea of this algorithm is that once computed the grobner representation the decoding step is pretty straight and it doesn't takes time. That's why I save the grobner representation as attribute of the code, so you only have to compute it once.
I also modified the format of the output for grobner_representation method. Now returns a dictionary representing Matphi function instead of a List.
GDDA and Grobner representation code
Here I leave you the comparison I've made of the GDDA with decoding algorithms already implemented in Sage such as "sydrome", "nearest neighbor" and guava.
The results are very interesting. I've tried with Hamming Codes, Extended Golay Code and random linear codes.
In the case with Hamming Code the GDDA resulted to be faster than "syndrome" ,"nearest neighbor" and "guava "algorithms, even considering the time it takes to compute grobner representation.
In case with random linear code GDDA resulted to be fasted that "syndrome" and "nearest neighbor" again even considering the time it takes to GDDA computing grobner representation.
With Extended Golay Code "syndrome" and "nearest neighbot" resulted to be faster than GDDA.