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Geometry of semilinear embeddings : relations to graphs and codes

Author: Mark Pankov
Publisher: New Jersey : World Scientific, [2015]
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

This volume covers semilinear embeddings of vector spaces over division rings and the associated mappings of Grassmannians.

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Document Type: Book
All Authors / Contributors: Mark Pankov
ISBN: 9789814651073 9814651079
OCLC Number: 900028793
Description: xii, 168 pages ; 24 cm
Contents: Semilinear Mappings: Division Rings and Their Homomorphisms; Vector Spaces Over Division Rings; Semilinear Mappings; Semilinear Embeddings; Mappings of Grassmannians Induced by Semilinear Embeddings; Kreuzer's Example; Duality; Characterization of Strong Semilinear Embeddings; Projective Geometry and Linear Codes: Projective Spaces; Fundamental Theorem of Projective Geometry; Proof of Theorem 1.2; m-independent Subsets in Projective Spaces; PGL-subsets; Generalized Macwilliams Theorem; Linear Codes; Remark on Symmetries of Linear Codes; Isometric Embeddings of Grassmann Graphs: Graph Theory; Elementary Properties of Grassmann Graphs; Embeddings; Isometric Embeddings; Proof of Theorem 3.1; Equivalence of Isometric Embeddings; Linearly Rigid Isometric Embeddings; Remarks on Non-isometric Embeddings; Some Results Related to Chow's Theorem; Huang's Theorem; Johnson Graph in Grassmann Graph: Johnson Graph; Isometric Embeddings of Johnson Graphs in Grassmann Graphs; Proof of Theorem 4.2; Classification Problem and Relations to Codes; Characterizations of Apartments in Building Grassmannians; Characterization of Isometric Embeddings: Result, Corollaries and Remarks; Special Subsets; Connectedness of the Apartment Graph; Intersections of J(n, k)-subsets of Different Types; Proof of Theorem 5.1; Semilinear Mappings of Exterior Powers: Exterior Powers; Grassmannians; Grassmann Codes;
Responsibility: Mark Pankov.

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