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Factorization of a class of polynomials over finite fields

✍ Scribed by Henning Stichtenoth; Alev Topuzoğlu


Book ID
113623072
Publisher
Elsevier Science
Year
2012
Tongue
English
Weight
198 KB
Volume
18
Category
Article
ISSN
1071-5797

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Generalizing the norm and trace mappings for % O P /% O , we introduce an interesting class of polynomials over "nite "elds and study their properties. These polynomials are then used to construct curves over "nite "elds with many rational points.

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Let T n (x, a) ʦ GF(q)[x] be a Dickson polynomial over the finite field GF(q) of either the first kind or the second kind of degree n in the indeterminate x and with parameter a. We give a complete description of the factorization of T n (x, a) over GF(q).