Algebraic geometric construction of a quantum stabilizer code

The stabilizer code is the most general algebraic construction of quantum error-correcting codes proposed so far. A stabilizer code can be constructed from a self-orthogonal subspace of a symplectic space over a finite field. We propose a construction method of such a selforthogonal space using an algebraic curve. By using the proposed method we construct an asymptotically good sequence of binary stabilizer codes that is better than the known sequences constructed from algebraic curves. The main results in this paper can be understood without knowledge of quantum mechanics.