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Register a new userNew Permutation Trinomials From Niho Exponents over Finite Fields with Even Characteristic
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Added by
Nian Li
Publication date
2016
fields
Informatics Engineering
and research's language is
English
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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.
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Motivated by recent results on the constructions of permutation polynomials with few terms over the finite field $mathbb{F}_{2^n}$, where $n$ is a positive even integer, we focus on the construction of permutation trinomials over $mathbb{F}_{2^n}$ from Niho exponents. As a consequence, several new classes of permutation trinomials over $mathbb{F}_{2^n}$ are constructed from Niho exponents based on some subtle manipulation of solving equations with low degrees over finite fields.
In this paper, we investigate the power functions $F(x)=x^d$ over the finite field $mathbb{F}_{2^{4n}}$, where $n$ is a positive integer and $d=2^{3n}+2^{2n}+2^{n}-1$. It is proved that $F(x)=x^d$ is APcN at certain $c$s in $mathbb{F}_{2^{4n}}$, and it is the second class of APcN power functions over finite fields of even characteristic. Further, the $c$-differential spectrum of these power functions is also determined.
In this paper, we produce new classes of MDS self-dual codes via (extended) generalized Reed-Solomon codes over finite fields of odd characteristic. Among our constructions, there are many MDS self-dual codes with new parameters which have never been reported. For odd prime power $q$ with $q$ square, the total number of lengths for MDS self-dual codes over $mathbb{F}_q$ presented in this paper is much more than those in all the previous results.
In this work we establish some new interleavers based on permutation functions. The inverses of these interleavers are known over a finite field $mathbb{F}_q$. For the first time M{o}bius and Redei functions are used to give new deterministic interleavers. Furthermore we employ Skolem sequences in order to find new interleavers with known cycle structure. In the case of Redei functions an exact formula for the inverse function is derived. The cycle structure of Redei functions is also investigated. The self-inverse and non-self-inver
Let $mathbb{F}_q$ denote the finite fields with $q$ elements. The permutation behavior of several classes of infinite families of permutation polynomials over finite fields have been studied in recent years. In this paper, we continue with their studies, and get some further results about the permutation properties of the permutation polynomials. Also, some new classes of permutation polynomials are constructed. For these, we alter the coefficients, exponents or the underlying fields, etc.
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