Coding for Modern Distributed Storage Systems II
summary
Continues the LRC story with explicit constructions and a concrete failure model: a Reed–Solomon variant picks a degree set skipping every (R+1)th monomial to get alphabet size linear in n and local groups from multiplicative cosets; maximal recoverability is defined as correcting every erasure pattern allowed by the topology. Random choices need huge fields; explicit constructions use linearized polynomials plus binary code parity checks to get roughly field size K^H and guarantee that puncturing one per column leaves MDS. Open problems: linear-size fields, tensor-code MR characterization, and tighter lower bounds.
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