GSoC Fifth Week (14-19 July)

This week the main goal was to implement the function that given a Binary Linear Code it returns

a reduced Grobner basis. 

We want the Grobner basis to later compute the test-set(see definition in the pdf). This structure is the last thing we'll need to then start programming the new decoding algorithm, which is the main objective of this project. 

Here I attach the explanation of the algorithm and also the way I use the implemented function. With some examples tested in Sage.  Algorithm  

Example tested with Sage

Here is the implementation of the function: Code

So far, I've tried to use what is already implemented in Sage. But one problem I presented with this function is that I need the permutations of one vector with given hamming weight. And I did it using "IntegerVectorsModPermutationGroup" nevertheless this part is very consuming time. And for codes which have a big length is not going to work. So, for the next week I'm planning to find another way of implementing this. At least for the binary case, which I think should be posible with bitwise operations.