On Quantum Stabilizer Codes derived from Local Frobenius Rings
Information Theory
2017-10-30 v1 math.IT
Rings and Algebras
Abstract
In this paper we consider stabilizer codes over local Frobenius rings. First, 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
Cite
@article{arxiv.1710.09884,
title = {On Quantum Stabilizer Codes derived from Local Frobenius Rings},
author = {Heide Gluesing-Luerssen and Tefjol Pllaha},
journal= {arXiv preprint arXiv:1710.09884},
year = {2017}
}