Constructions of Locally Recoverable Codes which are Optimal

06/29/2018

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by   Giacomo Micheli, et al.

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We provide a Galois theoretical framework which allows to produce good polynomials for the Tamo and Barg construction of optimal locally recoverable codes (LRC). Our approach allows to prove existence results and to construct new good polynomials, which in turn allows to build new LRCs. The existing theory of good polynomials fits in our new framework.