题目: Optimal locally repairable codes via automorphism groups of elliptic curves
摘要: Locally repairable codes, or locally recoverable codes (LRC for short) are designed for application in distributed and cloud storage systems. Similar to classical block codes, there is an important bound called the Singleton-type bound for locally repairable codes. A block code achieving this Singleton-type bound is referred to an optimal locally repairable code. Like classical MDS codes, optimal locally repairable codes have very nice combinatorial structures. In this talk, we will make use of automorphism groups of elliptic curves to present explicit constructions of optimal locally repairable codes. This is a joint work with Professor Chaoping Xing.
题目：Constructions of maximally recoverable local reconstruction codes
报告人：金玲飞 副教授 （复旦大学）
摘要：Local Reconstruction Codes (LRCs) allow for recovery from a small number of erasures in a local manner based on just a few other codeword symbols. They have emerged as the codes of choice for large scale distributed storage systems due to the very efficient repair of failed storage nodes in the typical scenario of a single or few nodes failing, while also offering fault tolerance against worst-case scenarios with more erasures. A maximally recoverable (MR) LRC offers the best possible blend of such local and global fault tolerance, guaranteeing recovery from all erasure patterns which are information-theoretically correctable given the presence of local recovery groups. In this talk, we intoduce an approach to construct MR LRCs. Our method recovers, and in most parameter regimes improves, the field size of previous approaches.
腾讯号：622 964 073