The dual geometry of Hermitian two-point codes

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• 作者：Edoardo Ballico ; Alberto Ravagnani
• 关键词：Hermitian code ; Goppa code ; Two-point code ; Minimum-weight codeword
• 刊名：Discrete Mathematics
• 出版年：2013
• 出版时间：6 December, 2013
• 年：2013
• 卷：313
• 期：23
• 页码：2687-2695
• 全文大小：416 K

文摘

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.