Generalized Reed-Muller codes and curves with many points

DOI10.1006/jnth.1998.2277zbMath0914.94019OpenAlexW1554949136MaRDI QIDQ1273721

Marcel van der Vlugt, Gerard van der Geer

Publication date: 23 March 1999

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.1998.2277

zbMATH Keywords

Reed-Muller codegeneralized Hamming weightHasse-Weil boundArtin-Schreier curve

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Curves over finite and local fields (11G20)

Related Items (9)

Another generalisation of the binary Reed-Muller codes and its applications ⋮ Artin-Schreier curves given by \(\mathbb{F}_q\)-linearized polynomials ⋮ Radon transforms and packings ⋮ Tables of curves with many points ⋮ Counting plane cubic curves over finite fields with a prescribed number of rational intersection points ⋮ Weight enumerators of Reed-Muller codes from cubic curves and their duals ⋮ Classification of all Galois subcovers of the Skabelund maximal curves ⋮ On curves covered by the Hermitian curve. ⋮ Curves of large genus covered by the hermitian curve

Cites Work

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• The genus of maximal function fields over finite fields
• Fibre products of Artin-Schreier curves and generalized Hamming weights of codes
• The genus of curves over finite fields with many rational points
• Generalized Hamming weights for linear codes
• How to Construct Curves over Finite Fields With Many Points
• Generalized Hamming weights of q-ary Reed-Muller codes
• Tables of curves with many points

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