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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.
Article history: Received 26 August 2013 Received in revised form 24 December 2013 Accepted 3 January 2014 Available online xxxx Communicated by Rudolf Lidl MSC: 11C08 12E10
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 DA(n), to be the least natural number k such that for any sequence (x1, · · · , xk) with xi ∈ G, there exists a non-empty subsequence (xj1, · · · , xjl) and a1, · · · , al ∈ A such that ∑l i=1 aixji = 0. Similarly, we define the constant… (More)
Recently, Tu and Deng obtained two classes of Boolean functions with nice properties based on a combinatorial conjecture about binary strings. In this paper, using different approaches, we prove this conjecture is true in several cases.
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 show that, if S contains no zero-sum subsequence and the group generated by all elements of S is not a cyclic group, then f (S) ≥ 2|S| − 1. Moreover, we… (More)