Structure of functional codes defined on non-degenerate Hermitian varieties

DOI10.1016/j.jcta.2011.05.006zbMath1230.94012OpenAlexW2007076829MaRDI QIDQ640852

San Ling, Frédéric A. B. Edoukou, Xing, Chaoping

Publication date: 21 October 2011

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcta.2011.05.006

zbMATH Keywords

Hermitian surfaceHermitian varietyfunctional codesdivisor of a codeweights of codes

Mathematics Subject Classification ID

Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (6)

A note on diagonal and Hermitian hypersurfaces ⋮ Intersections of the Hermitian surface with irreducible quadrics in \(\mathrm{PG}(3,q^2)\), \(q\) odd ⋮ On the functional codes defined by quadrics and Hermitian varieties ⋮ 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

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Functional codes arising from quadric intersections with Hermitian varieties
• Weight polarization and divisibility
• Minimum possible block length of a linear binary code for some distances
• Codes defined by forms of degree 2 on non-degenerate Hermitian varieties in \(\mathbb{P}^4(\mathbb{F}_q)\)
• The weight distribution of the functional codes defined by forms of degree 2 on Hermitian surfaces
• Divisibility of codes meeting the Griesmer bound
• Codes from flag varieties over a finite field
• Evaluation codes from smooth quadric surfaces and twisted Segre varieties
• Codes defined by forms of degree 2 on Hermitian surfaces and Sørensen's conjecture
• Weight congruence for p-ary cyclic codes
• Fundamentals of Error-Correcting Codes
• Hermitian Varieties in a Finite Projective Space PG(N, q²)
• On a Theorem of Ax

This page was built for publication: Structure of functional codes defined on non-degenerate Hermitian varieties