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

Producción científica: Article › revisión exhaustiva

4 Citas (Scopus)

Resumen

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.

Idioma original	English
Páginas (desde-hasta)	145-173
Número de páginas	29
Publicación	Finite Fields and Their Applications
Volumen	58
DOI	https://doi.org/10.1016/j.ffa.2019.04.004
Estado	Published - jul 2019

Nota bibliográfica

Publisher Copyright:
© 2019 Elsevier Inc.

Financiación

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.

Financiadores	Número del financiador
Simons Foundation	422479
Simons Foundation

ASJC Scopus subject areas

Theoretical Computer Science
Algebra and Number Theory
General Engineering
Applied Mathematics

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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.",

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

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AU - Pllaha, Tefjol

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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UR - https://www.scopus.com/pages/publications/85065087580#tab=citedBy

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VL - 58

SP - 145

EP - 173

JO - Finite Fields and Their Applications

JF - Finite Fields and Their Applications

ER -

On quantum stabilizer codes derived from local Frobenius rings

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