On quantum stabilizer codes derived from local Frobenius rings

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On quantum stabilizer codes derived from local Frobenius rings. / Gluesing-Luerssen, Heide; Pllaha, Tefjol.

In: Finite Fields and Their Applications, Vol. 58, 01.07.2019, p. 145-173.

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@article{ead2a76d52364352898f6e124ed1a49d,
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",
year = "2019",
month = "7",
day = "1",
doi = "10.1016/j.ffa.2019.04.004",
language = "English",
volume = "58",
pages = "145--173",
journal = "Finite Fields and Their Applications",
issn = "1071-5797",
publisher = "Academic Press Inc.",

}

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TY - JOUR

T1 - On quantum stabilizer codes derived from local Frobenius rings

AU - Gluesing-Luerssen, Heide

AU - Pllaha, Tefjol

PY - 2019/7/1

Y1 - 2019/7/1

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

UR - http://www.scopus.com/inward/record.url?scp=85065087580&partnerID=8YFLogxK

U2 - 10.1016/j.ffa.2019.04.004

DO - 10.1016/j.ffa.2019.04.004

M3 - Article

VL - 58

SP - 145

EP - 173

JO - Finite Fields and Their Applications

JF - Finite Fields and Their Applications

SN - 1071-5797

ER -

ID: 33833529