A polynomial construction of quantum codes with asymptotically nonzero rate and relative distance was presented using algebraic geometry codes. The generator matrix of the sympletic code was used to construct a polynomial complexity encoder, which is a sequence of Gaussian elimination of k×n matrices. It was shown that generator matrices of algebraic geometry codes can be constructed in polynomial time.
|Number of pages
|Physical Review A - Atomic, Molecular, and Optical Physics
|Published - Mar 2001