On quantum stabilizer codes derived from local Frobenius rings

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2 Scopus citations

Abstract

In this paper we consider stabilizer codes over local Frobenius rings. Firstly, we study the relative minimum distances of a stabilizer code and its reduction onto the residue field. We show that for various scenarios, a free stabilizer code over the ring does not underperform the according stabilizer code over the field. This leads us to conjecture that the same is true for all free stabilizer codes. Secondly, we focus on the isometries of stabilizer codes. We present some preliminary results and introduce some interesting open problems.

Original languageEnglish
Pages (from-to)145-173
Number of pages29
JournalFinite Fields and Their Applications
Volume58
DOIs
StatePublished - Jul 2019

Bibliographical note

Publisher Copyright:
© 2019 Elsevier Inc.

Keywords

  • Local Frobenius rings
  • Quantum stabilizer codes
  • Self-orthogonal codes
  • Symplectic isometries

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Algebra and Number Theory
  • General Engineering
  • Applied Mathematics

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