A polynomial f ∈ F q [ x ] is called a permutation polynomial (PP) if the induced polynomial function f: c ↦ f ( c ) from F q to itself permutes F q . A polynomial f ∈ F q [ x ] is called a complete permutation polynomial (CPP) if both f ( x ) and f ( x ) + x are permutations of F q .
A permutation polynomial f ( x ) over a finite field F q is called a complete permutation polynomial (see [2], [6], [9], [11]), or a complete mapping (see [5], ...
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Jun 15, 2018 · We construct several new classes of sparse permutation polynomials over \mathbb{F}_{q^3}, q=p^{k}, p\geq3. Some of them are complete mappings.
In mathematics, a permutation polynomial (for a given ring) is a polynomial that acts as a permutation of the elements of the ring, i.e. the map x ↦ g ( x ) ...
In this paper we determine $b\in\F_{q^n}^*$ for which the polynomial $f(x)=x^{s+1}+bx\in\F_{q^n}[x]$ is a permutation polynomial and determine $b\in\F_{q^n}^*$ ...
We further investigate nine classes of permutation polynomials over with the form and propose five classes of complete permutation polynomials over with the ...
If f ( x ) and f ( x ) + x permute F p m simultaneously, then f ( x ) is called a complete permutation polynomial (CPP). Permutation polynomials play important ...
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Several new classes of sparse permutation polynomials over Fq3 are constructed based on the multivariate method and resultant elimination, some of them are ...
Jun 26, 2019 · Introduction. Let q be a power of a prime number and let Fq be a finite field with q elements. A polynomial f(x) ∈ Fq[x].
Oct 14, 2023 · A permutation polynomial of is called a complete permutation polynomial (complete mapping) of if is also a permutation polynomial of . Complete ...