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Aug 28, 2016 at 21:54 comment added unknown yes, but I'm allowing any combination of $(U,V)$ in any order; here $V$ is a permutation of order $n$. So it's equivalence under a larger group containing $GL_k({\mathbb F}_2)$ and $S_n$ as subgroups. (general linear group and symmetric group). Two matrices equivalent under these operations generate equivalent codes (hence the coding theory tag).
Aug 28, 2016 at 21:17 comment added Robert Israel If a column permutation of $P$ is orthogonal, so is $P$.
Aug 28, 2016 at 19:41 comment added unknown I'm allowing these two types of operations : the first is multiply by invertible matrix $U$ : $ G \to U G = [I_k \mid P]$ and the second is a column permutations of $UG$ to make $P$ orthogonal (if possible).
Aug 28, 2016 at 18:37 comment added Robert Israel "Put into" by what operations?
Aug 27, 2016 at 21:16 history edited Michael Hardy CC BY-SA 3.0
added 6 characters in body
Aug 27, 2016 at 21:09 history asked unknown CC BY-SA 3.0