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We give, over a finite field F q , explicit factorizations into a product of irreducible polynomials, of the cyclotomic polynomials of order 3 · 2 n , the Dickson polynomials of the first kind of order 3 · 2 n and the Dickson polynomials of the second kind of order 3 · 2 n − 1.

We develop a matrix approach to compute a certain sum of Gauss sums which arises in the study of weights of irreducible codes. A lower bound on the minimum weight of certain irreducible codes is given.

Reversed Dickson polynomials over finite fields are obtained from Dickson polynomials D n (x, a) over finite fields by reversing the roles of the indeterminate x and the parameter a. We study reversed Dickson polynomials with emphasis on their permutational properties over finite fields. We show that reversed Dickson permutation polynomials (RDPPs) are… (More)

We give new descriptions of the factors of Dickson polynomials over finite fields.