Artin-Schreier curves and weights of two-dimensional cyclic codes

DOI10.1016/j.ffa.2003.10.002zbMath1096.94042OpenAlexW2034595612MaRDI QIDQ2566949

Cem Güneri

Publication date: 29 September 2005

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ffa.2003.10.002

zbMATH Keywords

Artin-Schreier curvetrace code2-D cyclic code

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items

Quasi-Cyclic Subcodes of Cyclic Codes, Bounds on quasi-cyclic codes over finite chain rings, Explicit maximal and minimal curves over finite fields of odd characteristics, On complementary dual additive cyclic codes, Some Artin-Schreier type function fields over finite fields with prescribed genus and number of rational places, Weight distributions of Q2DC codes over finite fields, 2-D skew-cyclic codes over \(\mathbb F_q[x,y;\rho ,\theta\)], A relation between quasi-cyclic codes and 2-D cyclic codes, Explicit maximal and minimal curves of Artin-Schreier type from quadratic forms, Multidimensional cyclic codes and Artin-Schreier type hypersurfaces over finite fields, A minimum distance bound for 2-dimension \(\lambda\)-quasi-twisted codes over finite fields, A minimum distance bound for quasi-\(n\)D-cyclic codes, Quadratic forms of codimension 2 over finite fields containing \(\mathbb F_4\) and Artin-Schreier type curves

Uses Software

• Macaulay2

Cites Work

• Unnamed Item
• Algebraic function fields and codes
• Weight distributions for a certain class of codes and maximal curves
• On minimum distance bounds for abelian codes
• Bounds for exponential sums over finite fields
• The Geometry of Two-Weight Codes
• The concatenated structure of cyclic and Abelian codes
• A theory of two-dimensional cyclic codes
• A BOUND ON THE NUMBER OF RATIONAL POINTS OF CERTAIN ARTIN-SCHREIER FAMILIES
• Algebraic-geometric codes and multidimensional cyclic codes: a unified theory and algorithms for decoding using Grobner bases
• Families of curves and weight distributions of codes