Vol. 6, No. 1, 2008

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The geometry of quantum codes

Jürgen Bierbrauer, Giorgio Faina, Massimo Giulietti, Stefano Marcugini and Fernanda Pambianco

Vol. 6 (2008), No. 1, 53–71
Abstract

We give a geometric interpretation of additive quantum stabilizer codes in terms of sets of lines in binary symplectic space. It is used to obtain synthetic geometric constructions and non-existence results. In particular several open problems are removed from Grassl’s database.

Mathematical Subject Classification 2000
Primary: 51E21, 94B05, 94B27, 94B60
Milestones
Received: 29 February 2008
Accepted: 14 May 2008
Authors
Jürgen Bierbrauer
Michigan Technological University
MI
United States
Giorgio Faina
Massimo Giulietti
Dipartimento di Matematica e Informatica
Università degli Studi di Perugia
Via Vanvitelli, 1
06123 Perugia
Italy
Stefano Marcugini
Fernanda Pambianco