Current Research Topics in Galois Geometry

Leo Storme and Jan De Beule (Editors)
Ghent University, Ghent, Belgium

Series: Mathematics Research Developments
BISAC: MAT012020

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Galois geometry is the theory that deals with substructures living in projective spaces over finite fields, also called Galois fields. This collected work presents current research topics in Galois geometry, and their applications. Presented topics include classical objects, blocking sets and caps in projective spaces, substructures in finite classical polar spaces, the polynomial method in Galois geometry, finite semifields, links between Galois geometry and coding theory, as well as links between Galois geometry and cryptography. (Imprint: Nova)

Preface
Jan De Beule (Ghent University, Department of Mathematics, Gent, Belgium) and Leo Storme (Ghent University, Department of Mathematics, Krijgslaan 281-S22, 9000 Ghent, Belgium)

Chapter 1. Constructions and Characterizations of Classical Sets in PG(n,q)
Frank De Clerck (Ghent University, Department of Mathematics, Ghent, Belgium), Nicola Durante (Dipartimento di Matematica e Applicazioni Caccioppoli, Università di Napoli “Federico II”, Napoli, Italy)

Chapter 2. Substructures of Finite Classical Polar Spaces
Jan De Beule and Andreas Klein (Ghent University, Department of Mathematics, Gent, Belgium), Klaus Metsch (Universität Gießen, Mathematisches Institut, Germany)

Chapter 3. Blocking Sets in Projective Spaces
Aart Blokhuis (Eindhoven University of Technology, Department of Mathematics and Computer Science, Eindhoven, The Netherlands), Péter Sziklai (Eötvös Loránd University, Institute of Mathematics, Budapest, Hungary), Tamás Szőnyi (Eötvös Loránd University, Institute of Mathematics, Budapest, Hungary and Computer and Automation Research Institute, Hungarian Academy of Sciences, Budapest, Hungary)

Chapter 4. Large Caps in Projective Galois Spaces
Jürgen Bierbrauer (Department of Mathematical Sciences, Michigan Technological University, Houghton, MI, USA), Yves Edel (Ghent University, Department of Mathematics, Gent, Belgium)

Chapter 5. The Polynomial Method in Galois Geometries
Simeon Ball (Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, Barcelona, Spain)

Chapter 6. Finite Semifields
Michel Lavrauw (Ghent University, Department of Mathematics, Gent, Belgium) and Olga Polverino (Dipartimento di Matematica, Seconda Università degli Studi di Napoli, Caserta, Italy)

Chapter 7. Codes Over Rings and Ring Geometries
Thomas Honold (Department of Information and Electronic Engineering, Zhejiang University, Hangzhou, China) and Ivan Landjev (New Bulgarian University, Sofia, Bulgaria and Institute of Mathematics and Informatics, Sofia, Bulgaria)

Chapter 8. Galois Geometries and Coding Theory
Ivan Landjev and Leo Storme (Ghent University, Department of Mathematics, Ghent, Belgium)

Chapter 9. Applications of Galois Geometry to Cryptology
Wen-Ai Jackson (School of Mathematical Sciences, The University of Adelaide, Australia), Keith M. Martin (Information Security Group, Royal Holloway, University of London, U.K) and Maura B. Paterson (Department of Economics, Mathematics and Statistics, Birkbeck, University of London, London, UK)

Chapter 10. Galois Geometries and Low-Density Parity-Check Codes
Marcus Greferath (School of Mathematical Sciences, University College Dublin, Dublin, Ireland), Cornelia Rößing (School of Mathematical Sciences, University College Dublin, Dublin, Ireland) and Leo Storme (Ghent University, Department of Mathematics, Ghent, Belgium)

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