2012/05/28 by Ballico, Edoardo, Ravagnani, Alberto
#Algebraic Geometry (math.AG) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.1205.6184
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.