Galois extensions and subspaces of alternating bilinear forms with special rank properties

DOI10.1016/j.laa.2008.11.021zbMath1211.15030arXiv0709.0741OpenAlexW2015191305MaRDI QIDQ1014486

Rachel Quinlan, Roderick Gow

Publication date: 29 April 2009

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0709.0741

zbMATH Keywords

Galois groupcyclic extensionGalois extensionpolynomialfieldconstant rankalternating bilinear form

Mathematics Subject Classification ID

Separable extensions, Galois theory (12F10) Bilinear and Hermitian forms (11E39) Quadratic and bilinear forms, inner products (15A63)

Related Items (20)

On the list decodability of rank-metric codes containing Gabidulin codes ⋮ \(r\)-fat linearized polynomials over finite fields ⋮ Extending two families of maximum rank distance codes ⋮ Linear sets on the projective line with complementary weights ⋮ A new family of linear maximum rank distance codes ⋮ On the number of inequivalent Gabidulin codes ⋮ Twisted linearized Reed-Solomon codes: a skew polynomial framework ⋮ On the number of roots of some linearized polynomials ⋮ New semifields and new MRD codes from skew polynomial rings ⋮ On certain linearized polynomials with high degree and kernel of small dimension ⋮ Multi-orbit cyclic subspace codes and linear sets ⋮ On the number of the rational zeros of linearized polynomials and the second-order nonlinearity of cubic Boolean functions ⋮ Spectra of Boolean Functions, Subspaces of Matrices, and Going Up Versus Going Down ⋮ Linearized trinomials with maximum kernel ⋮ A characterization of linearized polynomials with maximum kernel ⋮ Subspaces of matrices with special rank properties ⋮ Generalized twisted Gabidulin codes ⋮ Galois theory and linear algebra ⋮ On maximum additive Hermitian rank-metric codes ⋮ MRD codes with maximum idealizers

Cites Work

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• Nonemptiness of skew-symmetric degeneracy loci
• On two extremal matrix problems
• Alternating bilinear forms over GF(q)
• Bilinear forms over a finite field, with applications to coding theory
• On symmetric degeneracy loci, spaces of symmetric matrices of constant rank and dual varieties
• On the vanishing of subspaces of alternating bilinear forms

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