Codes from flag varieties over a finite field

DOI10.1016/S0022-4049(02)00188-3zbMath1021.94027OpenAlexW2024108989MaRDI QIDQ1861503

François Rodier

Publication date: 9 March 2003

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-4049(02)00188-3

zbMATH Keywords

algebraic-geometric codesfinite fieldsflag varietieserror-correcting codes

Mathematics Subject Classification ID

Grassmannians, Schubert varieties, flag manifolds (14M15) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27)

Related Items (9)

On codes over \(\mathrm{FFN}(1,q)\)-projective varieties ⋮ Linear codes associated to skew-symmetric determinantal varieties ⋮ AG codes on flag bundles over a curve ⋮ Structure of functional codes defined on non-degenerate Hermitian varieties ⋮ Higher Grassmann codes ⋮ On Lagrangian-Grassmannian codes ⋮ Varieties over finite fields: quantitative theory ⋮ Sums of residues on algebraic surfaces and application to coding theory ⋮ Codes defined by forms of degree 2 on non-degenerate Hermitian varieties in \(\mathbb{P}^4(\mathbb{F}_q)\)

Cites Work

• The parameters of projective Reed-Müller codes
• Linear codes and modular curves
• Number of points of Deligne-Lusztig surfaces
• Error-correcting codes from higher-dimensional varieties
• Projective Reed-Muller codes
• The weight hierarchy of higher dimensional Hermitian codes
• Reed-Muller codes on complete intersections.
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