780 research outputs found
Further Results on Permutation Polynomials over Finite Fields
Permutation polynomials are an interesting subject of mathematics and have
applications in other areas of mathematics and engineering. In this paper, we
develop general theorems on permutation polynomials over finite fields. As a
demonstration of the theorems, we present a number of classes of explicit
permutation polynomials on \gf_q
Permutations via linear translators
International audienceWe show that many infinite classes of permutations over finite fields can be constructedvia translators with a large choice of parameters. We first characterize some functionshaving linear translators, based on which several families of permutations are then derived. Extending the results of \cite{kyu}, we give in several cases thecompositional inverse of these permutations. The connection with complete permutations is also utilized to provide further infinite classes of permutations. Moreover, wepropose new tools to study permutations of the form and a few infinite classes of permutations of this form are proposed
Regular complete permutation polynomials over quadratic extension fields
Let be any positive integer which is relatively prime to and
. Let be any permutation polynomials over
is an invertible linear map over
and . In this paper,
we prove that, for suitable and , the map
could be -regular complete permutation polynomials over quadratic extension
fields.Comment: 10 pages. arXiv admin note: substantial text overlap with
arXiv:2212.1286
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