Projective geometry - from foundations to applications

@inproceedings{Beutelspacher1998ProjectiveG,
  title={Projective geometry - from foundations to applications},
  author={A. Beutelspacher and Ute Rosenbaum},
  year={1998}
}
1. Synthetic geometry 2. Analytic geometry 3. The representation theorems 4. Quadratic sets 5. Applications of geometry to coding theory 6. Applications of geometry in cryptography. 
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References

SHOWING 1-10 OF 110 REFERENCES
Geometry and Codes
1. Rational Codes.- 2. Decoding and Rational Approximations.- 3. Algebraic Curves.- 4. Generalized Jacobian Codes.- References.
Projective Geometries Over Finite Fields
1. Finite fields 2. Projective spaces and algebraic varieties 3. Subspaces 4. Partitions 5. Canonical forms for varieties and polarities 6. The line 7. First properties of the plane 8. Ovals 9.Expand
Applications of Finite Geometry to Cryptography
In this paper we survey several applications of classical geometric structures to cryptology. Particularly we shall deal with authentication schemes, threshold schemes, network problems andExpand
On the foundations of polar geometry
One of the two Buekenhout-Shult theorems for polar spaces required a finite rank assumption. Here we get rid of that restriction. Similarly, the polar spaces of possibly infinite rank having someExpand
A proof of the theorem of Pappus in finite Desarguesian affine planes
Without using the representation theorem and a theorem of J.H.M. WEDDERBURN we show that every finite Desarguesian affine plane is Pappian.
A defense of the honour of an unjustly neglected little geometry or a combinatorial approach to the projective plane of order five
In this paper, we consider the projective plane of order five from a combinatorial point of view. We shall see many of its properties (such as its uniqueness and existence, the order of the fullExpand
Finite projective spaces of three dimensions
This self-contained and highly detailed study considers projective spaces of three dimensions over a finite field. It is the second and core volume of a three-volume treatise on finite projectiveExpand
A First Course in Coding Theory
  • R. Hill
  • Mathematics, Computer Science
  • 1986
TLDR
This book provides an elementary yet rigorous introduction to the theory of error-correcting codes, based on courses given by the author over several years to advanced undergraduates and first-year graduated students. Expand
Cryptography - theory and practice
  • D. Stinson
  • Computer Science
  • Discrete mathematics and its applications series
  • 1995
TLDR
The object of the book is to produce a general, comprehensive textbook that treats all the essential core areas of cryptography. Expand
On the foundations of incidence geometry
The tremendous and sudden development of diagram geometries and related concepts such as chamber systems, combinatorial maps, incidence complexes (see for instance [2], [14], [15], [3]) and theirExpand
...
1
2
3
4
5
...