论文标题
二元性和LP的界限
Duality and LP Bounds for Codes with Locality
论文作者
论文摘要
我们启动对本地可回收代码的二元性理论的研究，重点是应用。我们根据双重代码来表征代码的局部性，并引入一类不变式，以完善经典的重量分布。在这种情况下，我们建立了类似于（但与Macwilliams截然不同）的二元定理。作为结果的应用，我们为本地可回收代码的参数获得了两个新界限，包括在多个实例中改善最佳可用界限的LP界限。
We initiate the study of the duality theory of locally recoverable codes, with a focus on the applications. We characterize the locality of a code in terms of the dual code, and introduce a class of invariants that refine the classical weight distribution. In this context, we establish a duality theorem analogous to (but very different from) a MacWilliams identity. As an application of our results, we obtain two new bounds for the parameters of a locally recoverable code, including an LP bound that improves on the best available bounds in several instances.
