Maximally Recoverable Local Reconstruction Codes (LRCs) are codes designed for distributed storage to provide maximum resilience to failures for a given amount of storage redundancy and locality. An\u00a0\\((n,r,h,a,g)\\)-MR LRC has\u00a0\\(n\\)\u00a0coordinates divided into\u00a0\\(g\\)\u00a0local groups of size\u00a0\\(r=n\/g\\), where each local group has `\\(a\\)‘ local parity checks and there are an additional `\\(h\\)‘ global parity checks. Such a code can correct `\\(a\\)‘ erasures in each local group and any\u00a0\\(h\\)\u00a0additional erasures. Constructions of MR LRCs over small fields is desirable since field size determines the encoding and decoding efficiency in practice. In this work, we give a new construction of\u00a0\\((n,r,h,a,g)\\)-MR-LRCs over fields of size\u00a0\\(q=O(n{)^{}_{h+(g-1)a-\u2308h\/g\u2309}}\\)\u00a0which generalizes a construction of Hu and Yekhanin (ISIT 2016). This improves upon state of the art when there are a small number of local groups, which is true in practical deployments of MR LRCs.<\/p>\n","protected":false},"excerpt":{"rendered":"
Maximally Recoverable Local Reconstruction Codes (LRCs) are codes designed for distributed storage to provide maximum resilience to failures for a given amount of storage redundancy and locality. An\u00a0-MR LRC has\u00a0\u00a0coordinates divided into\u00a0\u00a0local groups of size\u00a0, where each local group has `’ local parity checks and there are an additional `’ global parity checks. 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