Download E-books Arithmetic of Finite Fields: First International Workshop, WAIFI 2007, Madrid, Spain, June 21-22, 2007. Proceedings PDF

By Robert W. Fitzgerald, Joseph L. Yucas (auth.), Claude Carlet, Berk Sunar (eds.)

Specific factorizations, right into a manufactured from irreducible polynomials, over Fq of thecyclotomic polynomials Q2n(x) are given in [4] whilst q ≡ 1 (mod 4). The caseq ≡ three (mod four) is finished in [5]. right here we supply factorizations of Q2nr(x) the place ris top and q ≡ ±1 (mod r). particularly, this covers Q2n3(x) for all Fq ofcharacteristic now not 2, three. We observe this to get particular factorizations of the firstand moment sort Dickson polynomials of order 2n3 and 2n3 − 1 respectively.Explicit factorizations of sure Dickson polynomials were used to computeBrewer sums [1]. yet our uncomplicated motivation is interest, to determine what factorsarise. Of curiosity then is how the generalized Dickson polynomials Dn(x, b) arisein the criteria of the cyclotomic polynomials and the way the Dickson polynomialsof the 1st sort look within the components of either forms of Dickson polynomials.

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