Impure codes exceeding the pure bounds for quantum local recovery
Information Theory
2026-04-07 v1 math.IT
Quantum Physics
Abstract
Literature provides several bounds for quantum local recovery, which essentially consider the number of message qudits, the distance, the length, and the locality of the involved codes. We give a family of -affine variety codes that result in impure CSS codes. These quantum codes exceed several of the above mentioned bounds that apply to pure quantum locally recoverable codes. We also discuss a connection between bounds on quantum local recovery and on weight-constrained stabilizer codes.
Cite
@article{arxiv.2604.03569,
title = {Impure codes exceeding the pure bounds for quantum local recovery},
author = {Carlos Galindo and Fernando Hernando and Helena Martín-Cruz and Ryutaroh Matsumoto},
journal= {arXiv preprint arXiv:2604.03569},
year = {2026}
}