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Permutation polynomials have been a subject of study for a long time and have applications in many areas of science and engineering. However, only a small number of specific classes of permutation polynomials are described in the literature so far. In this paper we present a number of permutation trinomials over finite fields, which are of different forms.… (More)

For the cyclic group G = Z/nZ and any non-empty A ∈ Z. We define the Davenport constant of G with weight A, denoted by D A (n), to be the least natural number k such that for any sequence (x 1 , · · · , x k) with x i ∈ G, there exists a non-empty subsequence (x j 1 , · · · , x j l) and a 1 , · · · , a l ∈ A such that l i=1 a i x j i = 0. Similarly, we… (More)

Let G be a finite abelian group, and let S be a sequence of elements in G. Let f (S) denote the number of elements in G which can be expressed as the sum over a nonempty subsequence of S. In this paper, we slightly improve some results of [10] on f (S) and we show that for every zero-sum-free sequences S over G of length |S| = exp(G) + 2 satisfying f (S) 4… (More)

a r t i c l e i n f o a b s t r a c t Permutation polynomials are an interesting subject of mathematics and have applications in other areas of mathematics and engineering. In this paper, we develop general theorems on permutation polynomials over finite fields. As a demonstration of the theorems, we present a number of classes of explicit permutation… (More)

Four recursive constructions of permutation polynomials over GF(q 2) with those over GF(q) are developed and applied to a few famous classes of permutation polynomials. They produce infinitely many new permutation polynomials over GF(q 2 ℓ) for any positive integer ℓ with any given permutation polynomial over GF(q). A generic construction of permutation… (More)

Let G be a finite abelian group, and let S be a sequence of elements in G. Let f (S) denote the number of elements in G which can be expressed as the sum over a nonempty subsequence of S. In this paper, we determine all the sequences S that contains no zero-sum subsequences and f (S) ≤ 2|S| − 1. MSC: Primary 11B75; Secondary 11B50.