A locally recoverable code is an error-correcting code such that any erasure in a single coordinate of a codeword can be recovered from a small subset of other coordinates. In this article we develop an algorithm that computes a recovery structure as concise posible for an arbitrary linear code $\mathcal{ C}$ and a recovery method that realizes it. This algorithm also provides the locality and the dual distance of $\mathcal{ C}$. Complexity issues are studied as well. Several examples are included.

Categories: cs.IT math.IT

Computing sharp recovery structures for Locally Recoverable codes