论文标题
可从曲线的纤维产品中可用的本地可回收代码的最小距离和参数范围
Minimum Distance and Parameter Ranges of Locally Recoverable Codes with Availability from Fiber Products of Curves
论文作者
论文摘要
我们使用曲线的光纤产品构建具有可用性$ t \ geq 2 $的本地可回收代码的家族，确定许多家庭的确切最小距离，并证明了此类代码最小距离的一般定理。本文以这些家族的代码参数和纤维产品构建的探索结束。我们表明，纤维产品代码可以达到任意较大的速率和任意较小的相对缺陷，并与文献中的已知界限和重要结构相比。
We construct families of locally recoverable codes with availability $t\geq 2$ using fiber products of curves, determine the exact minimum distance of many families, and prove a general theorem for minimum distance of such codes. The paper concludes with an exploration of parameters of codes from these families and the fiber product construction more generally. We show that fiber product codes can achieve arbitrarily large rate and arbitrarily small relative defect, and compare to known bounds and important constructions from the literature.
