Constraint on Left Inverse of a Matrix in a Binary Finite Field

Uncategorized
Aug 16, 2021
G

Hello. Binary matrices consisting of zero and one may or may not have left inverse in GF(2). How can we impose the condition that a matrix has a left inverse in GF(2) in CVX? Regarding the fact that a square matrix has a determinant of zero or one.

M

Doesn’t sound (mixed-integer) convex to me. But if you or some algebra guru have a clever formulation, please present it.

Edit: See my later post.

G
Replying to #2

Thanks for your attention.

G
Replying to #2

Is it possible to use LU decomposition or Gaussian elimination inside the CVX block such that gf(2) rules are respected?

M

Perhaps the program to address the original question could be a feasibility problem (no objective, unless otherwise needed) consisting of the declaration of a bunch of binary variables and a bunch of linear constraints which would be the linearization of n^2 bilinear binary equality constraints enforcing L*M == eye(n), where L is the putative left inverse of the binary matrix M. I leave the details to you.

G

Thanks for your suggestion. I keep working on it until I get results.