Improving the next code

[Juan Grados]

How can I improve the time for the next code?. Basically, I want to solve a large undetermined binary linear system and then I need to calculate its hamming weight.

A = random_matrix(GF(2), 10, 12, density=0.55)

b = random_vector(GF(2), 10)

particular_soln = A.solve_right(b, check=False)

A_right_kernel = A.right_kernel()

for homogeneous_soln in A_right_kernel:

    v = (particular_soln + homogeneous_soln)

    print len(v.nonzero_positions())

--

---------------------------------------------------------------------
MSc. Juan del Carmen Grados Vásquez
Laboratório Nacional de Computação Científica 
Tel: +55 21 97633 3228

(http://www.lncc.br/)
http://juaninf.blogspot.com
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[David Joyner]

On Sun, Feb 25, 2018 at 4:11 PM, Juan Grados <jua...@gmail.com> wrote:
> How can I improve the time for the next code?. Basically, I want to solve a
> large undetermined binary linear system and then I need to calculate its
> hamming weight.
>
> A = random_matrix(GF(2), 10, 12, density=0.55)
> b = random_vector(GF(2), 10)
> particular_soln = A.solve_right(b, check=False)
> A_right_kernel = A.right_kernel()
> for homogeneous_soln in A_right_kernel:
> v = (particular_soln + homogeneous_soln)
> print len(v.nonzero_positions())
>

You are computing the min wt of a coset of a binary linear code.
I don't know of a fast stand alone function that does this.

Printing slows you down a lot. Just make the list of wts using list
comprehension and find its minimum later.

For real speed, you make want to modify the C code in
GAP's AClosestVectorCombinationsMatFFEVecFFE.

>
> --
> ---------------------------------------------------------------------
> MSc. Juan del Carmen Grados Vásquez
> Laboratório Nacional de Computação Científica
> Tel: +55 21 97633 3228
> (http://www.lncc.br/)
> http://juaninf.blogspot.com
> ---------------------------------------------------------------------
>

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[Juan Grados]

Thanks, David, 

I think that the problem is with the operation "+" I have using Profiler and when the matrix has dimensios, 12 x 19 these are the times

9.932s -- line 15: v = (particular_soln + homogeneous_soln)
0.004s -- line 17: print len(v.nonzero_positions())

Maybe there is some way to sum particular_soln + homogeneous_soln in a fast way?

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