Locally repairable codes have been extensively investigated due to practical applications in distributed and cloud storage systems in recent years. However, not much work on asymptotic behavior of locally repairable codes has been done. In particular, there is few result on constructive lower bound of asymptotic behavior of locally repairable codes with multiple recovering sets. In this paper, we construct some families of asymptotically good locally repairable codes with multiple recovering sets via automorphism groups of function fields of the Garcia-Stichtenoth towers. The main advantage of our construction is to allow more flexibility of localities.

翻译：近年来，局部可修复码因其在分布式存储和云存储系统中的实际应用而受到广泛研究。然而，关于局部可修复码渐近行为的研究尚不充分，特别是在具有多恢复集的局部可修复码的渐近行为构造性下界方面成果甚少。本文通过Garcia-Stichtenoth塔函数域的自同构群，构造了一系列渐近最优的具有多恢复集的局部可修复码族。我们构造的主要优势在于允许局部性具有更高的灵活性。