Functional codes arising from quadric intersections with Hermitian varieties

DOI10.1016/j.ffa.2009.11.005zbMath1219.94091OpenAlexW2082861357MaRDI QIDQ623249

Storme, L., Anja Hallez

Publication date: 14 February 2011

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

Full work available at URL: https://biblio.ugent.be/publication/956445

zbMATH Keywords

Hermitian varietiesquadricsfunctional codes

Mathematics Subject Classification ID

Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Linear codes and caps in Galois spaces (51E22) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (11)

The small weight codewords of the functional codes associated to non-singular Hermitian varieties ⋮ A note on diagonal and Hermitian hypersurfaces ⋮ Intersections of the Hermitian surface with irreducible quadrics in \(\mathrm{PG}(3,q^2)\), \(q\) odd ⋮ Galois geometries and coding theory ⋮ Tight sets in finite classical polar spaces ⋮ Structure of functional codes defined on non-degenerate Hermitian varieties ⋮ On the functional codes defined by quadrics and Hermitian varieties ⋮ On the functional codes arising from the intersections of algebraic hypersurfaces of small degree with a non-singular quadric ⋮ Linear codes from Denniston maximal arcs ⋮ A study of intersections of quadrics having applications on the small weight codewords of the functional codes \(C_2(Q)\), \(Q\) a non-singular quadric ⋮ Intersections of the Hermitian surface with irreducible quadrics in even characteristic

Cites Work

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• A study of intersections of quadrics having applications on the small weight codewords of the functional codes \(C_2(Q)\), \(Q\) a non-singular quadric
• Codes defined by forms of degree 2 on non-degenerate Hermitian varieties in \(\mathbb{P}^4(\mathbb{F}_q)\)
• Codes defined by forms of degree 2 on Hermitian surfaces and Sørensen's conjecture
• Some properties and applications of Hermitian varieties in a finite projective space PG(N,\(q^ 2\)) in the construction of strongly regular graphs (two-class association schemes) and block designs
• The small weight codewords of the functional codes associated to non-singular Hermitian varieties
• Hermitian Varieties in a Finite Projective Space PG(N, q²)

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