Efficient kernel-computing of sparse GF2 matrices

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Looking in sage/matrix/matrix_mod2_dense.pyx, I see that kernel_right uses the pluq algorithm, but otherwise I didn't see any other special implementations of kernel there. You could ask the sage-support list too.

I wouldn't necessarily expect other algorithms to be implemented, but here are some things you could try:

1. Try using the sparse=True keyword when you create the matrix; if better algorithms are available, this would be the generic way to use them: e.g. sparse matrices over Z/n for n small. (note that that documentation page doesn't mention kernel specifically.

2. If you know of an algorithm with a distinctive name, you could try searching the source code for it, using search_src, search_doc, or search_def

   sage: search_src('Euclidean')
   categories/basic.py:44:from euclidean_domains import EuclideanDomains
   categories/cartesian_product.py:169:        sage: EuclideanDomains().CartesianProducts()
   ...
   rings/all.py:37:from euclidean_domain_element import EuclideanDomainElement, is_EuclideanDomainElement
   rings/arith.py:1862:    very similar to the extended Euclidean algorithm. For more details,
   rings/arith.py:1896:        the extended Euclidean algorithm.)
   ...
   

3. Lastly, you could try reading some of the source files themselves: there are a number of likely filenames in sage/matrix.

And, of course, if you don't find the algorithm you're looking for, you could always implement it, and add it to sage!

good luck! :)