Fibre products of Artin-Schreier curves and generalized Hamming weights of codes

DOI10.1016/0097-3165(95)90099-3zbMath0824.94025OpenAlexW1989882541MaRDI QIDQ1805064

Marcel van der Vlugt, Gerard van der Geer

Publication date: 15 November 1995

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0097-3165(95)90099-3

zbMATH Keywords

trace codesrational pointsweight distributionsupersingular curvesgeneralized Hamming weightfibre product of Artin-Schreier curves

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (14)

On the weight hierarchy of the semiprimitive codes ⋮ Artin-Schreier curves given by \(\mathbb{F}_q\)-linearized polynomials ⋮ On the enumeration of irreducible polynomials over \(\mathrm{GF}(q)\) with prescribed coefficients ⋮ On the moments of Kloosterman sums and fibre products of Kloosterman curves ⋮ A new family of maximal curves over a finite field ⋮ Curves with many points and configurations of hyperplanes over finite fields ⋮ On generalized Hamming weights of \(\text{BCH}(2)^\perp\) ⋮ Generalized Reed-Muller codes and curves with many points ⋮ THE 2-RANKS OF HYPERELLIPTIC CURVES WITH EXTRA AUTOMORPHISMS ⋮ Walsh transforms of trace forms with three or more terms and some maximal Artin-Schreier curves ⋮ Codes on fibre products of some Kummer coverings ⋮ Imaginary bicyclic biquadratic function fields in characteristic two ⋮ Curves of every genus with many points. I: Abelian and toric families. ⋮ The number of rational points of a class of Artin-Schreier curves.

Cites Work

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• Artin-Schreier curves and codes
• Idempotent relations and factors of Jacobians
• Trace codes and families of algebraic curves
• Weight distributions for a certain class of codes and maximal curves
• The red book of varieties and schemes
• The effective length of subcodes
• Jodeit's extensions for bilinear multipliers (Bull. London Math Soc. 40 (2008) 937-944)
• Generalized Hamming weights for linear codes
• Generalized Hamming weights of trace codes
• Generalized Hamming Weights of Melas Codes and Dual Melas Codes
• The Second Generalized Hamming Weight of the Dual Codes of Double-Error Correcting Binary BCH-Codes

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