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On the number of rational points on codimension-1 algebraic sets in Pn(Fq)

✍ Scribed by Anders Bjært Sørensen

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
644 KB
Volume
135
Category
Article
ISSN
0012-365X

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✦ Synopsis

An upper bound on the number of F,-rational points on a pure (n -l)-dimensional algebraic set of low degree defined over F, in P(F,) is given, using simple counting arguments, and the result is generalized to all degrees using results from coding theory. The bound depends on n, q, d, where d is the degree of the algebraic set. A number of corollaries are deduced and applications to coding theory are mentioned.

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