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Solve large system of linear equations over GF(2)

asked 2011-03-28 14:10:14 -0600

ji-o gravatar image

I need to solve a pretty large system of linear equations over GF(2) (The matrix is around 20000 x 20000). The straightforward approach used to solve linear equation systems (by using MatrixSpace and octave) will ran out of memory before even building up the matrix.

I wonder if there is any method i could use to solve such a system. Also note that the system i try to solve is sparse in general.

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answered 2011-10-13 07:35:59 -0600

malb gravatar image

Hi,

20,000 x 20,000 is not large and you should be able to do it in a few seconds on a modern CPU:

http://m4ri.sagemath.org/performance.html

However, Sage doesn't expose the fast code we have for this in M4RI:, cf.

http://m4ri.sagemath.org/doxygen/solve_8h.html

That's why it's not as fast as it should be. Sorry, we should fix this.

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answered 2011-03-31 23:02:23 -0600

mmarco gravatar image

It's just a guess, but maybe a groebner basis over boolean algebra method would work. Look for documentation about the polybori interface.

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Asked: 2011-03-28 14:10:14 -0600

Seen: 1,127 times

Last updated: Oct 13 '11