Computing sharp recovery structures for Locally Recoverable codes

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 as possible 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.