AI 中文总结
本文针对无稳定器结构的纯不交 $(r,δ)$-量子局部可修复码，提出局部恢复条件与权枚举器，推导类 Singleton 界和码维上界，为该类码的研究提供新方法。
AI 中文摘要
我们研究不假设稳定器结构的纯不交 $(r,δ)$-量子局部可修复码（qLRCs）。我们针对在一个修复块内最多 $δ-1$ 个 erasures 的恢复，提出局部 Knill–Laflamme 条件，并引入分块 Shor–Laflamme 和酉权枚举器，以捕捉错误权在修复集间的分布情况。我们建立这些枚举器的若干性质，并用它们推导类 Singleton 界，该界在纯度假设下强化了已知的不交 $(r,δ)$-qLRCs 界，还推导了码维的线性规划上界。这些结果为研究纯不交 $(r,δ)$-qLRCs 提供了一种基于非稳定器、权枚举器的方法。
英文摘要
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.
CommentsAccepted for presentation at the 2026 IEEE International Symposium on Information Theory (ISIT 2026)
