Question: Solving System of Equations Mod 2

I want to solve a system of 11^3 equations  (each equation is quite small) in 11^2 unknows. The equations are all viewed mod 2. I only want to know the possible solutions for 11 of those variables.

That is given variables a[i], 1 from 1 to 11 and b[n] for the remaining 11^2-11  variables.

I want to know all the  distinct consistent solutions for the a[i]'s. I dont care what the b's are as long as the solution to the a[i]s is consistent.

I am VERY sure that the equations will quickly show that there are no solutions but I am having difficulty comming up with how to code this. 

 

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