How can I compute the inverse of a very large GF(2) matrix efficiently?!

I currently have a double matrix A of size 1282 x 1282 that consists only of ones and zeros, I want to calculate the inverse of matrix A over GF(2). I am trying to calculate its inverse in the following manner:

inv_A = inv(gf(A,2))

My problem is that this method works to find the inverse matrix of a small binary number, but for that size it is taking too long. Any ideas on how I can implement this more efficiently? I would truly appreciate some help.

[Bruno Luong]

Sorry not my domain of expertise, but it seems GF(2) is {0,1} field, where as MATLAB command gf(.,2) has 2^2 = 4 elements.

Doc

Which one are you working on?