منابع مشابه
Permutation Groups Generated by Binomials
Let G(q) be the group of permutations of Fq generated by those permutations which can be represented as c 7→ ac + bc with a, b ∈ Fq and 0 < m < n < q. We show that there are infinitely many q for which G(q) is the group of all permutations of Fq . This resolves a conjecture of Vasilyev and Rybalkin.
متن کاملPermutation Binomials over Finite Fields
We prove that if xm + axn permutes the prime field Fp, where m > n > 0 and a ∈ Fp, then gcd(m − n, p − 1) > √ p − 1. Conversely, we prove that if q ≥ 4 and m > n > 0 are fixed and satisfy gcd(m − n, q − 1) > 2q(log log q)/ log q, then there exist permutation binomials over Fq of the form xm + axn if and only if gcd(m,n, q − 1) = 1.
متن کاملNonexistence of Permutation Binomials of Certain Shapes
Suppose xm+axn is a permutation polynomial over Fp, where p > 5 is prime and m > n > 0 and a ∈ Fp. We prove that gcd(m−n, p−1) / ∈ {2, 4}. In the special case that either (p− 1)/2 or (p− 1)/4 is prime, this was conjectured in a recent paper by Masuda, Panario and Wang.
متن کاملA Generalized Lucas Sequence and Permutation Binomials
Let p be an odd prime and q = pm. Let l be an odd positive integer. Let p ≡ −1 (mod l) or p ≡ 1 (mod l) and l | m. By employing the integer sequence an = l−1 2 ∑ t=1 ( 2 cos π(2t− 1) l )n , which can be considered as a generalized Lucas sequence, we construct all the permutation binomials P (x) = xr + xu of the finite field Fq .
متن کاملNew classes of permutation binomials and permutation trinomials over finite fields
Permutation polynomials over finite fields play important roles in finite fields theory. They also have wide applications in many areas of science and engineering such as coding theory, cryptography, combinational design, communication theory and so on. Permutation binomials and trinomials attract people’s interest due to their simple algebraic form and additional extraordinary properties. In t...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 1990
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171290000497