GSoC Aug 18th - 25th

For this week I have implemented a new decoding algorithm for binary linear codes using Grobner
Basis of the ideal associated to the code.
In the binary case I have decided to use the FGLM algorithm from singular to compute the Grobner
Basis, this algorithm is very fast.  So first I have to construct the ideal associated to the code.
Then, I create a test-set for the code. And use this one to apply the descent decoding algorithm.
More details about this algorithm :  Theory
The process of computing the grobner basis and the test-set is only executed once, and after that, the decoding process is very fast.(Decoding algorithms with pre-computed information)
I have done some tests to analyze the time it takes with the different decoding algorithms and differents types of binary linear codes:
Results of experiments:  Testing Algorithm

Also I have documented the functions with examples and more. The code of this algorithm and functions is in the commit:
https://bitbucket.org/vsuaste/coding-theory/commits/4d5c8255eaec112b191eb095873eaf09e5708ed4

With this algorithm I finished algorithms for binary codes. So from now, I have started trying to generalize the algorithms for the case of codes over any finite field.
In this case we expect to gain some speed with a new version of FGLM algorithm implemented specificaly for general case of codes.

GSoC Aug 12th -16th

For this week I have fixed some details about documentation:
https://bitbucket.org/vsuaste/coding-theory/commits/6b81bda12ea08dbb5fd11d35f786f240#comment-379372

I have implemented a new function for computing grobner basis for a binary linear Code.
I noticed that my results and the results using package 4ti2 are not the same, and this is because of the order of the variables. 4ti2 consider xn> ... >x0 and the order I use is x0>x1>x2...
In sage you can compute the grobner basis of an ideal, but you can specify the order of the variables. By default it uses x0>x1>x2>...
Fortunately this detail doesn't matter for our purposes(decoding algorithm) as long as the monomial order is a degree order and therefore a weight compatible order.
Here it goes an Example
And code: Code
(Once I finish the documentation for this one I'll uploaded to bitbucket, also the output format will be changed because of the way I'll use it for the decoding algorithm using grobner basis)