Higher Hamming weights for locally recoverable codes on algebraic curves

We study the locally recoverable codes on algebraic curves. In the first part of this article, we provide a bound of generalized Hamming weight of these codes. Whereas in the second part, we propose a new family of algebraic geometric LRC codes, that are LRC codes from Norm-Trace curve. Finally, using some properties of Hermitian codes, we improve the bounds of distance proposed in [1] for some Hermitian LRC codes. [1] A. Barg, I. Tamo, and S. Vlladut. Locally recoverable codes on algebraic curves. arXiv preprint arXiv:1501.04904, 2015

Locally recoverable J-affine variety codes

A locally recoverable (LRC) code is a code over a finite eld Fq such that any erased coordinate of a codeword can be recovered from a small number of other coordinates in that codeword. We construct LRC codes correcting more than one erasure, which are sub eld-subcodes of some J-affine variety codes. For these LRC codes, we compute localities (r; )) that determine the minimum size of a set R of positions so that any - 1 erasures in R can be recovered from the remaining r coordinates in this set. We also show that some of these LRC codes with lengths n >> q are ( - 1)-optimal