Weight enumerators of Reed-Muller codes from cubic curves and their duals

DOI10.1090/conm/722/14535zbMath1429.94088arXiv1809.09176OpenAlexW2894153765MaRDI QIDQ5236838

Nathan Kaplan

Publication date: 16 October 2019

Published in: Arithmetic Geometry: Computation and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.09176

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Curves over finite and local fields (11G20) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (1)

Counting plane cubic curves over finite fields with a prescribed number of rational intersection points

Cites Work

• Weight enumeration of codes from finite spaces
• Cubic curves, finite geometry and cryptography
• Hecke operators and the weight distributions of certain codes
• The parameters of projective Reed-Müller codes
• Nonsingular plane cubic curves over finite fields
• Generalized Reed-Muller codes and curves with many points
• Hecke polynomials as congruence \(\zeta\) functions in elliptic modular case
• Die Typen der Multiplikatorenringe elliptischer Funktionenkörper
• Traces of Hecke operators and refined weight enumerators of Reed-Solomon codes
• Fundamentals of Error-Correcting Codes
• Projective Reed-Muller codes
• Weight Formulas for Ternary Melas Codes
• Generalized Hamming weights of q-ary Reed-Muller codes
• Elliptic curves over a finite field and the trace formula
• Families of curves and weight distributions of codes
• Cayley-Bacharach theorems and conjectures
• How the Number of Points of An Elliptic Curve Over a Fixed Prime Field Varies
• Abelian varieties over finite fields
• On generalized ReedMuller codes and their relatives
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