Enhancements to GF(2) Linear Algebra: in-place row echelon with pivots, nullspace, and basis for row space

[Fe-r-oz]

This PR implements enhancements to the GF(2) Linear Algebra functionality. Inspired by python comprehensive ldpc.mod2 functionality. The following functionality are implemented in simple Julia:

1. gf2_row_echelon_with_pivots!: return row echelon form, transformation matrix, rank and pivots
2. gf2_nullspace: null space
3. gf2_rowspace_basis: basis of the row space

Motivation: Currently, we don't have pure linear algebra implementation of the logical X and logical Z operators for stabilizer CSS code without using MixedDestabilizer. Meaning, we can determine the logicals that satisfy the following conditions:

1. $L_z \in \ker(H_x)$
2. $L_z \notin \text{Im}(H_z^T)$

And

1. $L_x \in \ker(H_z)$
2. $L_x \notin \text{Im}(H_x^T)$

These tools are going to be useful for pure linear algebra implementation of logical operators for CSS stabilizer codes. In general, I think it would nice to have complete set of GF(2) functionality. I have tested for correctness and also add consistency check with ldpc

Edit:

When the nullity is 0, a vector is zeros is convention. In this case, the ldpc.mod2.nullspace returns []. I have followed the convention.

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• All new functionality is tested.
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[Fe-r-oz]

Please help review this PR, Thank you!