Name
Abstract | ||
|---|---|---|
In this paper, we construct several new classes of complete permutation monomials a−1xd over a finite field Fqn with exponents d=qn−1q−1+1, qp−1−1q−1+1, and qq−1−1q−1+1, respectively, where q=pk is a power of a prime number p. Our approach uses the AGW criterion (the multiplicative case) together with Dickson permutation polynomials and a class of exceptional polynomials respectively. One of our results confirms Conjecture 4.18 by G. Wu, N. Li, T. Helleseth, Y. Zhang in [42] under the assumption that the characteristic p is primitive modulo a prime number n+1. Moreover, we show that Conjecture 4.18 is false in general using our approach and a counterexample is provided. We also re-confirm Conjecture 4.20 in [42] that was proved recently in [24], and extend some of these recent results to more general n's and more general a's. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1016/j.ffa.2019.01.003 | Finite Fields and Their Applications |
Keywords | Field | DocType |
11T06,05A05,11T55 | Finite field,Combinatorics,Prime number,Polynomial,Multiplicative function,Permutation,Monomial,Counterexample,Conjecture,Mathematics | Journal |
Volume | ISSN | Citations |
57 | 1071-5797 | 2 |
PageRank | References | Authors |
0.38 | 3 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xiutao Feng | 1 | 61 | 9.93 |
| Dongdai Lin | 2 | 762 | 98.54 |
| Li-Ping Wang | 3 | 49 | 6.83 |
| Qiang Wang | 4 | 237 | 37.93 |