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In this paper, by using a powerful criterion for permutation polynomials given by Zieve, we give several classes of complete permutation monomials over Fqr. In addition, we present a class of complete permutation multinomials, which is a generalization of recent work.
Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, several classes of p-ary linear codes with two or three weights are constructed from quadratic Bent functions over the finite field F p , where p is an odd prime. They include some earlier linear codes as… (More)
Several new classes of binary and <i>p</i>-ary regular bent functions are obtained in this paper. The bentness of all these functions is determined by some exponential sums over finite fields, most of which have close relations with the well-known Kloosterman sums.
Linear codes with a few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of constructing two-weight and three-weight linear codes of Ding et al. and Zhou et al. to general weakly regular bent… (More)
Let m ≥ 3 be an odd integer and p be an odd prime. In this paper, a number of classes of three-weight cyclic codes C(1,e) over F<sub>p</sub>, which have parity-check polynomial m<sub>1</sub>(x)m<sub>e</sub>(x), are presented by examining general conditions on the parameters p, m, and e, where m<sub>i</sub>(x) is the minimal polynomial of π-i… (More)
This paper follows the recent work of Helleseth, Kholosha, Johansen, and Ness to study the cross correlation between an m -sequence of period 2<sup>m</sup> - 1 and the d-decimation of an m-sequence of a shorter period 2<sup>n</sup> - 1 for an even number m = 2n. Assuming that d satisfies d(2<sup>l</sup> + 1) = 2<sup>i</sup> (mod 2<sup>n</sup> - 1) for some… (More)