Codes defined by forms of degree 2 on non-degenerate Hermitian varieties in \(\mathbb{P}^4(\mathbb{F}_q)\)

DOI10.1007/s10623-008-9219-1zbMath1247.05046arXivmath/0612229OpenAlexW2080324276MaRDI QIDQ1009101

Frédéric A. B. Edoukou

Publication date: 31 March 2009

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0612229

zbMATH Keywords

weightsminimum distanceHermitian varietydistribution of codewordsfunctional codes of second orderquadratic section

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Rational points (14G05) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Combinatorial aspects of finite geometries (05B25)

Related Items (5)

Intersections of the Hermitian surface with irreducible quadrics in \(\mathrm{PG}(3,q^2)\), \(q\) odd ⋮ Functional codes arising from quadric intersections with Hermitian varieties ⋮ Structure of functional codes defined on non-degenerate Hermitian varieties ⋮ Intersections of the Hermitian surface with irreducible quadrics in even characteristic ⋮ Sums of residues on algebraic surfaces and application to coding theory

Cites Work

• The ubiquity of order domains for the construction of error control codes
• Error-correcting codes from higher-dimensional varieties
• Codes from flag varieties over a finite field
• 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
• Some Results on Quadrics in Finite Projective Geometry Based on Galois Fields
• Projective Reed-Muller codes
• Hermitian Varieties in a Finite Projective Space PG(N, q²)
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