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Dickson Polynomials and Irreducible Polynomials Over Finite Fields

โœ Scribed by S.H. Gao; G.L. Mullen

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
523 KB
Volume
49
Category
Article
ISSN
0022-314X

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Let k=GF(q) be the finite field of order q. Let f 1 (x), f 2 (x) # k[x] be monic relatively prime polynomials satisfying n=deg f 1 >deg f 2 0 and f 1 (x)ร‚f 2 (x){ g 1 (x p )ร‚g 2 (x p ) for any g 1 (x), g 2 (x) # k[x]. Write Q(x)= f 1 (x)+tf 2 (x) and let K be the splitting field of Q(x) over k(t). L

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Let T n (x, a) สฆ 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).