26 research outputs found
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
On the Hermitian curve and its intersections with some conics
We classify completely the intersections of the Hermitian curve with
parabolas in the affine plane. To obtain our results we employ well-known
algebraic methods for finite fields and geometric properties of the curve
automorphisms. In particular, we provide explicit counting formulas that have
also applications to some Hermitian codes.Comment: This article is contained in previous article "On the Hermitian
curve, its intersections with some conics and their applications to
affine-variety codes and Hermitian codes" (arXiv:1208.1627