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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 Thas
Apart 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 Applications

ISSN

1071-5797

Publisher

Elsevier

Volume

32

Page range

44-81

Department affiliated with

  • Mathematics Publications

Notes

Special Issue : Second Decade of FFA

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2015-12-16

First Compliant Deposit (FCD) Date

2015-12-16

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