Proof confirms maximum size for binary linear subspace codes
A proof of the Braun-Etzion-Vardy bound for binary subspace codes
Information Theory
Summary
Subspace codes are special sets used in coding theory to handle errors in data transmission. Braun, Etzion, and Vardy guessed these sets can only reach a certain size, specifically 2 to the power of n elements. This paper confirms their guess is true by using a new mathematical proof based on character theory. The proof is complete on its own and does not need outside results.
What this means in practice
- •For network designers: Design more efficient network error-correcting codes by knowing the exact maximum size of certain linear subspace codes.
- •For quantum computing teams: Inform the development of quantum error correction schemes that leverage binary subspace code limits confirmed by this proof.
A theory result. No direct application yet.
Authors
Srikanth B. Pai
Abstract
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.