quantum error-correcting codes , coding theory , algebraic geometry
Abstract:
An explicit construction for nonbinary quantum Goppa codes (often also called quantum AG codes) exceeding the quantum Gilbert-Varshamov bound is given. First a weighted symplectic inner product is introduced and a method how to transform weighted codes into quantum codes with respect to the standard symplectic inner product is given. Then families of quantum Goppa codes using a tower of function fields by Stichtenoth are constructed. Finally a proof that these codes lie above the quantum Gilbert-Varshamov bound is given.
Additional information:
Das Dokument wird vom Publikationsserver der Universitätsbibliothek Mannheim bereitgestellt.