On quantum stabilizer codes derived from local Frobenius rings

Heide Gluesing-Luerssen*, Tefjol Pllaha

*Corresponding author for this work

Research output: Contribution to journalArticle

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
Publication statusPublished - 1 Jul 2019
MoE publication typeA1 Journal article-refereed

Keywords

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

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