AI 中文总结
本文提出基于矩的新型Delsarte型线性规划界，适用于各类(r,δ)-局部可恢复码，在二元、三元字母表上的计算显示其可强化现有界。
AI 中文摘要
本文推导了q元(r,δ)-局部可恢复码（LRC）的新型Delsarte型线性规划界，具有三个属性：其一，变量集规模与经典Delsarte线性规划的变量集规模相当；其二，该线性规划通过阶δ-2挖掘局部距离条件强制的高阶信息，对于非退化线性码，其平衡基部分给出的维数界与Gruica、Jany和Ravagnani的对称化精化重量线性规划完全相同，且当δ≥3时非空的额外约束可进一步强化该界；其三，该线性规划适用于一般(r,δ)-LRC，包括线性与非线性类型。在二元和三元字母表上的大量计算表明，凸包线性规划取得了先前线性规划未捕捉到的改进，且常能缩短并强化广义Singleton界。
英文摘要
In this paper we derive new Delsarte-type linear programming bounds for $q$-ary $(r,δ)$-locally recoverable codes (LRCs) with three attributes: first, the variable set is comparable in size to that of the classical Delsarte LP; second, our LP exploits the higher-order information forced by the local-distance condition through order \(δ-2\), in the sense that for nondegenerate linear codes, its balanced base part gives exactly the same dimension bound as the symmetrized refined-weight LP of Gruica, Jany, and Ravagnani, while the additional constraints, nonvacuous whenever $δ\ge 3$, give a further strengthening; and third, it applies to general $(r,δ)$-LRCs, linear and nonlinear alike. Extensive computations over binary and ternary alphabets show that the convex-hull LP yields improvements not captured by the previous LP and often sharpens the shortening and generalized Singleton bounds.
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