3 research outputs found
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
A general construction of regular complete permutation polynomials
Let be a positive integer and the finite field with
elements. In this paper, we consider the -regular complete permutation
property of maps with the form where
is a PP over an extension field and is an
invertible linear map over . We give a general construction
of -regular PPs for any positive integer . When is additive, we
give a general construction of -regular CPPs for any positive integer .
When is not additive, we give many examples of regular CPPs over the
extension fields for and for arbitrary odd positive integer .
These examples are the generalization of the first class of -regular CPPs
constructed by Xu, Zeng and Zhang (Des. Codes Cryptogr. 90, 545-575 (2022)).Comment: 24 page