Minimum distance of Hermitian two-point codes

2009/02/01 by Seungkook Park, Park, Seungkook
Computer Science · Engineering · Mathematics · #11T71 #14G50 #94B40 #Algebraic Geometry (math.AG) #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #graph theory and CDMA systems #math.AG #math.NT #msc:11T71 #msc:14G50 #msc:94B40

paper · pdf · doi:10.48550/arxiv.0902.0135

21 pages

arxiv created 2009/02/01 · openalex publication_date 2009/02/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a formula for the minimum distance of two-point codes on a Hermitian curve.

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• The dual geometry of Hermitian two-point codes
• Improved Two-Point Codes on Hermitian Curves
• On the minimum distance and the minimum weight of Goppa codes from a quotient of the Hermitian curve
• On the geometry of Hermitian one-point codes
• A Generalized Floor Bound for the Minimum Distance of Geometric Goppa Codes and its Application to Two-Point Codes