报告人：葛根年  （首都师范大学教授）

时间：2020.11.15 9:30-10:30

腾讯会议信息：

会议 ID：818 180 412

报告摘要：

In recent years, the rapidly increasing amounts of data created and processed through the internet resulted in distributed storage systems employing erasure coding based schemes. Among these schemes, several classes of codes were introduced to balance the tradeoff between faulttolerance and system reliability, among which locally repairable codes (LRCs) play an important role. Furthermore, in order to provide maximal data recovery for correlated failures with efficient encoding and decoding, as a generalization of LRCs, maximally recoverable codes came up. Most known constructions are over large fields with sizes close to the code length, which lead to the systems being computationally expensive. Hence, codes over small sized fields are of interest in practice.

In this talk, we will focus on the constructions of locally repairable codes and maximally repairable codes over small sized fields. We will provide some new constructions for binary optimal LRCs with disjoint repair groups, employing partial spreads. We will also give a complete determination for the existence of optimal (n, k, r)-LRCs over the quaternary field. Finally, we will present the first polynomial upper bound on the field size needed for achieving the maximal recoverability of codes with topologies Tm×n(1, b, 0), using the Combinatorial Nullstellensatz and the hypergraph independent set approaches.

邀请人：汪馨