A construction of Locally Recoverable Codes

Locally Recoverable Codes (LRCs) are a popular topic lately, in particular for their potential applications in distributed storage.  The
locality consists in the possibility of recovering one corrupted symbol using a small amount of other symbols.
In this talk, we give a new construction of such codes. We start by giving an example reaching the Singleton-like bound for LRCs using polynomials and Reed-Solomon codes. We investigate similarities with certain concatenated codes. Contrary to previous methods, our construction allows one to obtain directly codes whose dimension is not a multiple of the locality. We finally explains that the general frame of these codes is the generalization of AG codes of Xing, Niederreiter and Lam introduced in 1999.