纯量子$(r,ρ)$局部可恢复码的字母相关界
Alphabet-Dependent Bounds for Pure Quantum $(r,ρ)$-Locally Recoverable Codes
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中文总结 AI 辅助
本文针对纯量子$(r,ρ)$局部可恢复码，通过Hermitian CSS构造推导了三个字母相关的上界，确立了其渐近层级关系并明确了各界的最严格约束区域，解决了现有与字母无关的界在中小维度时宽松的问题。
中文摘要 AI 辅助
量子$(r,ρ)$局部可恢复码（$(r,ρ)$-qLRC）是一种量子码，其中每个量子位可从至多$r+ρ-1$个其他量子位恢复，即便恢复集内还有$ρ-1$个额外擦除。目前这类码的已知界包括类Singleton界和类GG Singleton界，它们与字母无关，因此在量子位维度较小至中等时较为宽松。本文中，我们通过Hermitian CSS构造推导了纯$(r,ρ)$-qLRC的三个字母相关上界：类Griesmer界、类Plotkin界和类球填充界。我们进一步确立了这些界之间的渐近层级关系，并确定了每个界能给出最严格码率约束的相对距离区域。
英文摘要
A quantum $(r,ρ)$-locally recoverable code ($(r,ρ)$-qLRC) is a quantum code in which every qudit can be recovered from at most $r+ρ-1$ other qudits, even after $ρ-1$ additional erasures inside the recovery set. The bounds currently known for this class, namely the Singleton-like and the GG Singleton-like bounds, are alphabet independent and are therefore loose for small-to-moderate qudit dimensions. In this letter, we derive three alphabet-dependent upper bounds for pure $(r,ρ)$-qLRCs obtained through the Hermitian CSS construction: a Griesmer-like, a Plotkin-like, and a sphere-packing-like bound. We further establish the asymptotic hierarchy among these bounds and identify the relative-distance regions in which each of them yields the tightest rate constraint.
发表机构
- International Institute of Information Technology（印度信息技术国际学院）
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