The minimum storage rack-aware regenerating (MSRR) code is a variation of regenerating codes that achieves the optimal repair bandwidth for a single node failure in the rack-aware model. The authors in~\cite{Chen-Barg2019} and~\cite{Zhou-Zhang2021} provided explicit constructions of MSRR codes for all parameters to repair a single failed node. This paper generalizes the results in~\cite{Chen-Barg2019} to the case of multiple node failures. We propose a class of MDS array codes and scalar Reed-Solomon (RS) codes, and show that these codes have optimal repair bandwidth and error resilient capability for multiple node failures in the rack-aware storage model. Besides, our codes keep the same access level as the low-access constructions in~\cite{Chen-Barg2019} and~\cite{Zhou-Zhang2021}.
Rack-Aware MSR Codes with Linear Field Size and Smaller Sub-Packetization for Tolerating Multiple Erasures
Key Lab of Education Blockchain and Intelligent Technology, Ministry of Education(教育部教育区块链与智能技术重点实验室);Guangxi Key Lab of Multi-source Information Mining & Security, Guangxi Normal University(广西师范大学多源信息挖掘与安全广西壮族自治区重点实验室);School of Mathematics and Statistics, Nanning Normal University(南宁师范大学数学与统计学院);The Center for Applied Mathematics of Guangxi (Guangxi Normal University)(广西应用数学中心(广西师范大学))
Reducing The Sub-packetization Level of Optimal-Access Cooperative MSR Codes
Ministry of Education Key Laboratory of Mathematics and Information Networks, School of Mathematical Sciences, Beijing University of Posts and Telecommunications(北京邮电大学数学与信息技术教育部重点实验室);School of Information Science and Engineering, Shandong Agricultural University(山东农业大学信息科学与工程学院)
Optimal-Access Cooperative MSR Codes: Parity-Check Matrix Construction And a Unified Transformation
Ministry of Education Key Laboratory of Mathematics and Information Networks, School of Mathematical Sciences, Beijing University of Posts and Telecommunications(北京邮电大学数学与信息技术教育部重点实验室);School of Information Science and Engineering, Shandong Agricultural University(山东农业大学信息科学与工程学院)
Maximally recoverable codes with locality and availability
IMUVa-Mathematics Research Institute, University of Valladolid(瓦拉多利德大学数学研究所);Signal Processing and Communications Research Center (SPCRC), International Institute of Information Technology, Hyderabad(海得拉巴国际信息学院信号处理与通信研究中心)