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)
In this paper, we follow the recent work of Helleseth, Kholosha, Johanssen and Ness to study the cross correlation between an m-sequence of period 2 m − 1 and the d-decimation of an m-sequence of shorter period 2 n − 1 for an even number m = 2n. Assuming that d satisfies d(2 l + 1) = 2 i (mod 2 n − 1) for some l and i, we prove the cross correlation takes… (More)
Let m ≥ 3 be an odd integer and p be an odd prime. In this paper, many classes of three-weight cyclic codes over F p are presented via an examination of the condition for the cyclic codes C (1,d) and C (1,e) , which have parity-check polynomials m 1 (x)m d (x) and m 1 (x)m e (x) respectively, to have the same weight distribution, where m i (x) is the… (More)
Cyclic codes are an important subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics. In this paper, two families of optimal ternary cyclic codes are presented. The first family of cyclic codes has parameters [3 m − 1, 3 m − 1 − 2m, 4] and contains a class of conjectured cyclic codes and… (More)