Quantum generalized Reed-Solomon codes: Unified framework for quantum MDS codes
Zhuo Li, Li-Juan Xing, and Xin-Mei Wang
TL;DR
This paper introduces a unified framework for quantum MDS codes based on classical generalized Reed-Solomon codes, providing conditions for their existence, bounds, and analytical construction methods.
Contribution
It develops a comprehensive construction and characterization of quantum MDS codes using generalized Reed-Solomon codes, unifying existing quantum MDS codes under this framework.
Findings
Quantum MDS codes can be constructed from classical GRS codes.
A necessary and sufficient condition for the existence of these quantum codes is derived.
The framework unifies previously known quantum MDS codes.
Abstract
We construct a new family of quantum MDS codes from classical generalized Reed-Solomon codes and derive the necessary and sufficient condition under which these quantum codes exist. We also give code bounds and show how to construct them analytically. We find that existing quantum MDS codes can be unified under these codes in the sense that when a quantum MDS code exists, then a quantum code of this type with the same parameters also exists. Thus as far as is known at present, they are the most important family of quantum MDS codes.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.