The dual geometry of Hermitian two-point codes

Edoardo Ballico; Alberto Ravagnani

doi:10.1016/j.disc.2013.08.014

The dual geometry of Hermitian two-point codes

Edoardo Ballico
, Alberto Ravagnani

Research output: Contribution to journal › Article › Academic › peer-review

4 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	2687-2695
Number of pages	9
Journal	Discrete Mathematics
Volume	313
Issue number	23
DOIs	https://doi.org/10.1016/j.disc.2013.08.014
Publication status	Published - 2013
Externally published	Yes

Funding

The first author was partially supported by MIUR and GNSAGA .

Keywords

Goppa code
Hermitian code
Minimum-weight codeword
Two-point code

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10.1016/j.disc.2013.08.014

Cite this

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title = "The dual geometry of Hermitian two-point codes",

abstract = "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.",

keywords = "Goppa code, Hermitian code, Minimum-weight codeword, Two-point code",

author = "Edoardo Ballico and Alberto Ravagnani",

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T1 - The dual geometry of Hermitian two-point codes

AU - Ballico, Edoardo

AU - Ravagnani, Alberto

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Goppa code

KW - Hermitian code

KW - Minimum-weight codeword

KW - Two-point code

UR - https://www.scopus.com/pages/publications/84883474696

U2 - 10.1016/j.disc.2013.08.014

DO - 10.1016/j.disc.2013.08.014

M3 - Article

AN - SCOPUS:84883474696

SN - 0012-365X

VL - 313

SP - 2687

EP - 2695

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 23

ER -

The dual geometry of Hermitian two-point codes

Abstract

Funding

Keywords

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