The Projectivization Matroid of a \(\boldsymbol{q}\) -Matroid

DOI10.1137/22m1494567zbMath1517.05034arXiv2204.01232OpenAlexW4377967046MaRDI QIDQ6161560

Benjamin Jany

Publication date: 27 June 2023

Published in: SIAM Journal on Applied Algebra and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.01232

zbMATH Keywords

characteristic polynomialweak mapsstrong mapsrank metric code\(q\)-matroidscritical theoremprojectivization matroid

Mathematics Subject Classification ID

Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) (52B40) Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Combinatorial aspects of matroids and geometric lattices (05B35)

Cites Work

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• Characteristic polynomials of weighted lattices
• Defining the \(q\)-analogue of a matroid
• The category of matroids
• Constructions of new \(q\)-cryptomorphisms
• \(q\)-polymatroids and their relation to rank-metric codes
• Linear cutting blocking sets and minimal codes in the rank metric
• Rank-metric codes and \(q\)-polymatroids
• Extensions of the critical theorem
• Independent spaces of \(q\)-polymatroids
• Weight Enumeration and the Geometry of Linear Codes
• Theory of Matroids

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