Xiang Fan

collaborators

Showing math.NTShow all

5 papers · 1 filter

math.NT2019

Permutation polynomials of degree 8 over finite fields of odd characteristic

Xiang Fan

This paper provides an algorithmic generalization of Dickson's method of classifying permutation polynomials (PPs) of a given degree $d$ over finite fields. Dickson's idea is to fo…

math.NT2019

Permutation polynomials of degree 8 over finite fields of characteristic 2

Xiang Fan

Up to linear transformations, we obtain a classification of permutation polynomials (PPs) of degree $8$ over $F_{2^{r}}$ with $r > 3$ . By [J. Number Theory 176 (2017) 466-66],…

math.NT2018

The Weil bound and non-exceptional permutation polynomials over finite fields

Xiang Fan

A well-known result of von zur Gathen asserts that a non-exceptional permutation polynomial of degree $n$ over $F_{q}$ exists only if $q < n^{4}$ . With the help of the Weil…

math.NT2018

A classification of permutation polynomials of degree $7$ over finite fields

Xiang Fan

Up to linear transformations, we give a classification of all permutation polynomials of degree $7$ over $F_{q}$ for any odd prime power $q$ , with the help of the SageMath…

math.NT2018

Linear complexity of Ding-Helleseth generalized cyclotomic sequences of order eight

Yana Liang, Jiali Cao, Xingfa Chen +2

During the last two decades, many kinds of periodic sequences with good pseudo-random properties have been constructed from classical and generalized cyclotomic classes, and used a…

Permutation polynomials of degree 8 over finite fields of odd characteristic

Permutation polynomials of degree 8 over finite fields of characteristic 2

The Weil bound and non-exceptional permutation polynomials over finite fields

A classification of permutation polynomials of degree 7 over finite fields

Linear complexity of Ding-Helleseth generalized cyclotomic sequences of order eight

A classification of permutation polynomials of degree $7$ over finite fields