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

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

URL: http://arxiv.org/abs/2608.10922v1
Date: Tue, 11 Aug 2026 13:48:28 GMT
Title: Bounds for Pure Disjoint $(r,δ)$-Quantum Locally Recoverable Codes
Abstract summary: We study pure disjoint $(r,)$-quantum locally recoverable codes (qLRCs) without assuming a stabilizer structure.<n>We formulate local Knill--Laflamme conditions for recovery from up to $-1$ erasures within a recovery block.<n>We introduce blockwise Shor--Laflamme and unitary weight enumerators that capture how error weight is distributed across recovery sets.
Score: 37.00616293796624
License: http://creativecommons.org/licenses/by/4.0/
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.

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