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arXiv:2608.10922 · IEEE International Symposium on Information Theory (ISIT)

Bounds for Pure Disjoint $(r,δ)$-Quantum Locally Recoverable Codes

Evagoras Stylianou, Holger Boche

cs.ITquant-phSubmitted Aug 11, 2026• Announced Aug 12, 2026• 0 citations
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Abstract

We study pure disjoint $(r,δ)$-quantum locally recoverable codes (qLRCs) without assuming a stabilizer structure. We formulate local Knill--Laflamme conditions for recovery from up to $δ-1$ erasures within a recovery block, and introduce blockwise Shor--Laflamme and unitary weight enumerators that capture how error weight is distributed across recovery sets. We establish several properties of these enumerators and use them to derive a Singleton-like bound that strengthens the known bound for disjoint $(r,δ)$-qLRCs under a purity assumption, as well as a linear-programming upper bound on the code dimension. These results provide a non-stabilizer, weight-enumerator-based approach to the study of pure disjoint $(r,δ)$-qLRCs.

Comments
Accepted for presentation at the 2026 IEEE International Symposium on Information Theory (ISIT 2026)

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