Innovations in Incidence Geometry

The geometry of quantum codes

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

Full-text: Open access

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.

Article information

Source
Innov. Incidence Geom., Volume 6-7, Number 1 (2007), 53-71.

Dates
Received: 29 February 2008
Accepted: 14 May 2008
First available in Project Euclid: 28 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.iig/1551323170

Digital Object Identifier
doi:10.2140/iig.2008.6.53

Mathematical Reviews number (MathSciNet)
MR2515258

Zentralblatt MATH identifier
1171.51304

Subjects
Primary: 51E21: Blocking sets, ovals, k-arcs 94B05: Linear codes, general 94B27: Geometric methods (including applications of algebraic geometry) [See also 11T71, 14G50] 94B60: Other types of codes

Keywords
quantum codes symplectic geometry Hermitian form additive codes Blokhuis-Brouwer construction APN function spread quantum cap

Citation

Bierbrauer, Jürgen; Faina, Giorgio; Giulietti, Massimo; Marcugini, Stefano; Pambianco, Fernanda. The geometry of quantum codes. Innov. Incidence Geom. 6-7 (2007), no. 1, 53--71. doi:10.2140/iig.2008.6.53. https://projecteuclid.org/euclid.iig/1551323170


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References

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