Finite geometry and the Gale transform
The Gale transform is an involution on sets of points in a projective space. It plays a crucial role in several different subjects, such as algebraic geometry, optimization, coding theory, etc. Sometimes, in the literature, the Gale transform is used implicitly, without mentioning it as such. In the...
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| Published in | Discrete mathematics Vol. 310; no. 22; pp. 3206 - 3210 |
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| Main Authors | , |
| Format | Journal Article Conference Proceeding |
| Language | English |
| Published |
Kidlington
Elsevier B.V
28.11.2010
Elsevier |
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| Online Access | Get full text |
| ISSN | 0012-365X 1872-681X |
| DOI | 10.1016/j.disc.2009.08.019 |
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| Abstract | The Gale transform is an involution on sets of points in a projective space. It plays a crucial role in several different subjects, such as algebraic geometry, optimization, coding theory, etc. Sometimes, in the literature, the Gale transform is used implicitly, without mentioning it as such. In the present paper, we give a short account of the algebraic and geometrical implications that the Gale transform has when it is applied to sets of points in finite projective spaces. |
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| AbstractList | The Gale transform is an involution on sets of points in a projective space. It plays a crucial role in several different subjects, such as algebraic geometry, optimization, coding theory, etc. Sometimes, in the literature, the Gale transform is used implicitly, without mentioning it as such. In the present paper, we give a short account of the algebraic and geometrical implications that the Gale transform has when it is applied to sets of points in finite projective spaces. |
| Author | Sonnino, Angelo Cossidente, Antonio |
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| Keywords | Gale transform Cap Projective space Coding theory Optimization method Discrete mathematics Combinatorics Algebraic geometry Optimization |
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| References | Dembowski (b2) 1997 Eisenbud, Popescu (b4) 2000; 230 Bosma, Cannon, Playoust (b1) 1997; 24 Dixon, Mortimer (b3) 1996; vol. 163 Hirschfeld, Thas (b5) 1991 Hirschfeld (10.1016/j.disc.2009.08.019_b5) 1991 Eisenbud (10.1016/j.disc.2009.08.019_b4) 2000; 230 Bosma (10.1016/j.disc.2009.08.019_b1) 1997; 24 Dixon (10.1016/j.disc.2009.08.019_b3) 1996; vol. 163 Dembowski (10.1016/j.disc.2009.08.019_b2) 1997 |
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| SubjectTerms | Algebra Algebraic geometry Cap Coding Combinatorics Combinatorics. Ordered structures Exact sciences and technology Functional analysis Gale transform Geometry Mathematical analysis Mathematics Optimization Projective space Sciences and techniques of general use Transforms |
| Title | Finite geometry and the Gale transform |
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