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Open problems in finite projective spaces
journal contribution
posted on 2023-06-08, 23:46 authored by J W P Hirschfeld, J A ThasApart from being an interesting and exciting area in combinatorics with beautiful results, finite projective spaces or Galois geometries have many applications to coding theory, algebraic geometry, design theory, graph theory, cryptology and group theory. As an example, the theory of linear maximum distance separable codes (MDS codes) is equivalent to the theory of arcs in PG(n, q); so all results of Section 4 can be expressed in terms of linear MDS codes. Finite projective geometry is essential for finite algebraic geometry, and finite algebraic curves are used to construct interesting classes of codes, the Goppa codes, now also known as algebraic geometry codes. Many interesting designs and graphs are constructed from fi- nite Hermitian varieties, finite quadrics, finite Grassmannians and finite normal rational curves. Further, most of the objects studied in this paper have an interesting group; the classical groups and other finite simple groups appear in this way.
History
Publication status
- Published
File Version
- Published version
Journal
Finite Fields and Their ApplicationsISSN
1071-5797Publisher
ElsevierExternal DOI
Volume
32Page range
44-81Department affiliated with
- Mathematics Publications
Notes
Special Issue : Second Decade of FFAFull text available
- No
Peer reviewed?
- Yes