On quantum stabilizer codes derived from local Frobenius rings

Heide Gluesing-Luerssen; Tefjol Pllaha

doi:10.1016/j.ffa.2019.04.004

On quantum stabilizer codes derived from local Frobenius rings

Heide Gluesing-Luerssen, Tefjol Pllaha

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	145-173
Number of pages	29
Journal	Finite Fields and Their Applications
Volume	58
DOIs	https://doi.org/10.1016/j.ffa.2019.04.004
State	Published - Jul 2019

Bibliographical note

Funding Information:
HGL was partially supported by the grant #422479 from the Simons Foundation. We would like to thank the reviewer for her/his very close reading and excellent comments.

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
Engineering (all)
Applied Mathematics

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10.1016/j.ffa.2019.04.004

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title = "On quantum stabilizer codes derived from local Frobenius rings",

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.",

keywords = "Local Frobenius rings, Quantum stabilizer codes, Self-orthogonal codes, Symplectic isometries",

author = "Heide Gluesing-Luerssen and Tefjol Pllaha",

note = "Funding Information: HGL was partially supported by the grant #422479 from the Simons Foundation. We would like to thank the reviewer for her/his very close reading and excellent comments. Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

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AU - Gluesing-Luerssen, Heide

AU - Pllaha, Tefjol

N1 - Funding Information: HGL was partially supported by the grant #422479 from the Simons Foundation. We would like to thank the reviewer for her/his very close reading and excellent comments. Publisher Copyright: © 2019 Elsevier Inc.

PY - 2019/7

Y1 - 2019/7

N2 - 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.

AB - 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.

KW - Local Frobenius rings

KW - Quantum stabilizer codes

KW - Self-orthogonal codes

KW - Symplectic isometries

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EP - 173

ER -

On quantum stabilizer codes derived from local Frobenius rings

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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