Rank properties of subspaces of symmetric and Hermitian matrices over finite fields

DOI10.1016/j.ffa.2011.03.001zbMath1233.15002OpenAlexW1971164824MaRDI QIDQ650826

John Sheekey, Jean-Guillaume Dumas, Roderick Gow

Publication date: 7 December 2011

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

Full work available at URL: https://doi.org/10.1016/j.ffa.2011.03.001

zbMATH Keywords

finite fieldrankHermitian matrixsymmetric matrixcommon zerosmatrixconstant rank subspace

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Hermitian, skew-Hermitian, and related matrices (15B57) Algebraic systems of matrices (15A30) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (6)

Non-linear maximum rank distance codes ⋮ Hermitian rank distance codes ⋮ Constant rank-distance sets of Hermitian matrices and partial spreads in Hermitian polar spaces ⋮ Symmetric bilinear forms over finite fields with applications to coding theory ⋮ On symmetric and Hermitian rank distance codes ⋮ From Independent Sets and Vertex Colorings to Isotropic Spaces and Isotropic Decompositions: Another Bridge between Graphs and Alternating Matrix Spaces

Cites Work

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• Subspaces of matrices with special rank properties
• On symmetric degeneracy loci, spaces of symmetric matrices of constant rank and dual varieties
• Pencils of quadratic forms over finite fields
• Pairs of quadratic forms

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