Quantum locally recoverable code with intersecting recovery sets

TL;DR

This paper introduces quantum locally recoverable codes with intersecting recovery sets, deriving bounds, constructing examples via hypergraph products, and applying these methods to improve classical LRC results, advancing quantum error correction understanding.

Contribution

It presents the concept of intersecting recovery sets in quantum LRCs, derives a singleton-like bound, and offers a new construction method using hypergraph products.

Findings

Derived a singleton-like bound for qLRCs with intersecting recovery sets.

Constructed qLRCs using a variation of the hypergraph product.

Improved classical LRC results using quantum code techniques.

Abstract

We introduce the concept of quantum locally recoverable codes (qLRCs) with intersecting recovery sets. We derive a singleton-like bound for these codes by leveraging the additional information provided by the intersecting recovery sets. Furthermore, we provide a construction for qLRCs with intersecting recovery sets by introducing a variation of the hypergraph product. Finally, we apply our qLRC methods to obtain improved results for classical LRCs. These results may provide new insights into the locality of quantum error correction code.