On the duals of geometric Goppa codes from norm-trace curves
Abstract
In this paper we study the dual codes of a wide family of evaluation codes on norm-trace curves. We explicitly find out their minimum distance and give a lower bound for the number of their minimum-weight codewords. A general geometric approach is performed and applied to study in particular the dual codes of one-point and two-point codes arising from norm-trace curves through Goppa's construction, providing in many cases their minimum distance and some bounds on the number of their minimum-weight codewords. The results are obtained by showing that the supports of the minimum-weight codewords of the studied codes obey some precise geometric laws as zero-dimensional subschemes of the projective plane. Finally, the dimension of some classical two-point Goppa codes on norm-trace curves is explicitly computed.
Keywords
Cite
@article{arxiv.1205.6184,
title = {On the duals of geometric Goppa codes from norm-trace curves},
author = {Edoardo Ballico and Alberto Ravagnani},
journal= {arXiv preprint arXiv:1205.6184},
year = {2013}
}
Comments
Finite Fields and their Applications, vol. 20 (2013), pp. 30-39