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Erasure Codes for Distributed Storage: Tight Bounds and Matching Constructions
This thesis makes several significant contributions to the theory of both
Regenerating (RG) and Locally Recoverable (LR) codes. The two principal
contributions are characterizing the optimal rate of an LR code designed to
recover from erased symbols sequentially, for any and the development
of a tight bound on the sub-packetization level (length of a vector code
symbol) of a sub-class of RG codes called optimal-access RG codes. There are
however, several other notable contributions as well such as deriving the
tightest-known bounds on the performance metrics such as minimum distance and
rate of a sub-class of LR codes known as availability codes. The thesis also
presents some low field size constructions of Maximal Recoverable codes.Comment: My PhD Thesi