The dual geometry of Hermitian two-point codes

被引：3
|
作者：
Ballico, Edoardo [1 ]
Ravagnani, Alberto [2 ]
机构：
[1] Univ Trento, Dept Math, I-38123 Povo, TN, Italy
[2] Univ Neuchatel, Inst Math, CH-2000 Neuchatel, Switzerland
来源：
DISCRETE MATHEMATICS | 2013年 / 313卷 / 23期
关键词：
Hermitian code; Goppa code; Two-point code; Minimum-weight codeword; MINIMUM DISTANCE; CURVE;
D O I：
10.1016/j.disc.2013.08.014
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the algebraic geometry of any two-point code on the Hermitian curve and reveal the purely geometric nature of their dual minimum distance. We describe the minimum-weight codewords of many of their dual codes through an explicit geometric characterization of their supports. In particular, we show that they appear as sets of collinear points in many cases. (C) 2013 Elsevier B.V. All rights reserved.
引用
收藏
页码：2687 / 2695
页数：9
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