19 research outputs found
New 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, combinatorial 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 this paper, several new classes of permutation
binomials and permutation trinomials are constructed. Some of these permutation
polynomials are generalizations of known ones.Comment: 18 pages. Submitted to a journal on Aug. 15t
A conjecture on permutation trinomials over finite fields of characteristic two
In this paper, by analyzing the quadratic factors of an -th degree
polynomial over the finite field \ftwon, a conjecture on permutation
trinomials over \ftwon[x] proposed very recently by Deng and Zheng is
settled, where and is a positive integer with
New Permutation Trinomials From Niho Exponents over Finite Fields with Even Characteristic
In this paper, a class of permutation trinomials of Niho type over finite
fields with even characteristic is further investigated. New permutation
trinomials from Niho exponents are obtained from linear fractional polynomials
over finite fields, and it is shown that the presented results are the
generalizations of some earlier works
On a Class of Permutation Trinomials in Characteristic 2
Recently, Tu, Zeng, Li, and Helleseth considered trinomials of the form
, where is even and
. They found sufficient conditions on for to be
a permutation polynomial (PP) of and they conjectured that the
sufficient conditions are also necessary. The conjecture has been confirmed by
Bartoli using the Hasse-Weil bound. In this paper, we give an alternative
solution to the question. We also use the Hasse-Weil bound, but in a different
way. Moreover, the necessity and sufficiency of the conditions are proved by
the same approach
Further results on complete permutation monomials over finite fields
In this paper, we construct some new classes of complete permutation
monomials with exponent using AGW criterion (a special
case). This proves two recent conjectures in [Wuetal2] and extends some of
these recent results to more general 's
Permutation Polynomials with Carlitz Rank 2
Let denote the finite field with elements. The Carlitz
rank of a permutation polynomial is a important measure of complexity of the
polynomial. In this paper we find the sharp lower bound for the weight of any
permutation polynomial with Carlitz rank , improving the bound found by
G\'omez-P\'erez, Ostafe and Topuzo\u{g}lu in that case.Comment: 10 pages, comments are welcom
Permutation trinomials over
We consider four classes of polynomials over the fields ,
, , ,
, ,
, where . We determine
conditions on the pairs and we give lower bounds on the number of pairs
for which these polynomials permute
A new class of permutation trinomials constructed from Niho exponents
Permutation polynomials over finite fields are an interesting subject due to
their important applications in the areas of mathematics and engineering. In
this paper we investigate the trinomial
over the finite field , where is an odd prime and
with being a positive integer. It is shown that when or ,
is a permutation trinomial of if and only if is even.
This property is also true for more general class of polynomials
, where is a
nonnegative integer and . Moreover, we also show that for
the permutation trinomials proposed here are new in the sense that
they are not multiplicative equivalent to previously known ones of similar
form.Comment: 17 pages, three table
Constructions and necessities of some permutation polynomials
Permutation polynomials over finite fields have important applications in
many areas of science and engineering such as coding theory, cryptography,
combinatorial design, etc. In this paper, we construct several new classes of
permutation polynomials, and the necessities of some permutation polynomials
are studied.Comment: 1
New Permutation Trinomials Constructed from Fractional Polynomials
Permutation trinomials over finite fields consititute an active research due
to their simple algebraic form, additional extraordinary properties and their
wide applications in many areas of science and engineering. In the present
paper, six new classes of permutation trinomials over finite fields of even
characteristic are constructed from six fractional polynomials. Further, three
classes of permutation trinomials over finite fields of characteristic three
are raised. Distinct from most of the known permutation trinomials which are
with fixed exponents, our results are some general classes of permutation
trinomials with one parameter in the exponents. Finally, we propose a few
conjectures