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.
A covering array CA(N ; t, k, v) is an N × k array such that every N × t sub-array contains all t-tuples from v symbols at least once, where t is the strength of the array. Covering arrays are used to generate software test suites to cover all t-sets of component interactions. The particular case when t = 2 (pairwise coverage) has been extensively studied,… (More)
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)