On the duals of geometric Goppa codes from norm-trace curves

作     者：Ballico, Edoardo Ravagnani, Alberto 

作者机构：Univ Trent Dept Math I-38123 Povo TN Italy Univ Neuchatel Dept Math CH-2000 Neuchatel Switzerland 

出 版 物：《FINITE FIELDS AND THEIR APPLICATIONS》 (Finite Fields Appl.)

年 卷 期：2013年第20卷第Mar.期

页      面：30-39页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：MIUR GNSAGA 

主　　题：Norm-trace curve Minimum distance Minimum-weight codeword 

摘      要：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 explicitely computed. (C) 2012 Elsevier Inc. All rights reserved.