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

页码：2687 / 2695

页数：9

共 50 条

[21] Two-Point AG Codes on the GK Maximal Curves
Castellanos, Alonso Sepulveda
Tizziotti, Guilherme Chaud
IEEE TRANSACTIONS ON INFORMATION THEORY, 2016, 62 (02) : 681 - 686
[22] RARE two-point Dixon with dual bandwidths
Ryden, Henric
Berglund, Johan
Norbeck, Ola
Avventi, Enrico
Sprenger, Tim
van Niekerk, Adam
Skare, Stefan
MAGNETIC RESONANCE IN MEDICINE, 2020, 84 (05) : 2456 - 2468
[23] One- and Two-Point Codes Over Kummer Extensions
Castellanos, Alonso S.
Masuda, Ariane M.
Quoos, Luciane
IEEE TRANSACTIONS ON INFORMATION THEORY, 2016, 62 (09) : 4867 - 4872
[24] Two Classes of Hermitian Dual-Containing BCH Codes and Their Applications
Li J.
Gao N.
Huang S.
Tien Tzu Hsueh Pao/Acta Electronica Sinica, 2022, 50 (11): : 2773 - 2777
[25] Two-Point AG Codes From One of the Skabelund Maximal Curves
Landi, Leonardo
Timpanella, Marco
Vicino, Lara
IEEE TRANSACTIONS ON INFORMATION THEORY, 2024, 70 (07) : 4792 - 4798
[26] The Hermitian Dual Codes of Several Classes of BCH Codes
Fan, Mengyuan
Li, Chengju
Ding, Cunsheng
IEEE TRANSACTIONS ON INFORMATION THEORY, 2023, 69 (07) : 4484 - 4497
[27] Automorphisms of Hermitian generalized algebraic geometry codes
Picone, Alberto
JOURNAL OF PURE AND APPLIED ALGEBRA, 2016, 220 (05) : 1935 - 1945
[28] The geometry of Hermitian self-orthogonal codes
Ball, Simeon
Vilar, Ricard
JOURNAL OF GEOMETRY, 2022, 113 (01)
[29] The geometry of Hermitian self-orthogonal codes
Simeon Ball
Ricard Vilar
Journal of Geometry, 2022, 113
[30] Multivariate Two-Point Padé-Type and Two-Point Padé Approximants
J. Abouir
A. Cuyt
R. Orive
Numerical Algorithms, 2003, 33 : 11 - 26

← 1 2 3 4 5 →