Higher Hamming weights for locally recoverable codes on algebraic curves

Abstract

We study locally recoverable codes on algebraic curves. In the first part of the manuscript, we provide a bound on the generalized Hamming weight of these codes. In the second part, we propose a new family of algebraic geometric LRC codes, which are LRC codes from the Norm-Trace curve. Finally, using some properties of Hermitian codes, we improve the bounds on the distance proposed in Barg et al. (2015) [1] of some Hermitian LRC codes.