A proof of the Braun-Etzion-Vardy bound for binary subspace codes

The notion of a linear subspace code in a projective space was introduced by Braun, Etzion and Vardy (2013), who conjectured that a linear subspace code in the projective space has at most 2^n codewords. We resolve this conjecture. A novel character-theoretic argument is used to prove the conjecture and the proof is self-contained.