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- W4313197166 abstract "Let $rgeq 3$ be a positive integer and $mathbb{F}_q$ the finite field with $q$ elements. In this paper, we consider the $r$-regular complete permutation property of maps with the form $f=taucircsigma_Mcirctau^{-1}$ where $tau$ is a PP over an extension field $mathbb{F}_{q^d}$ and $sigma_M$ is an invertible linear map over $mathbb{F}_{q^d}$. We give a general construction of $r$-regular PPs for any positive integer $r$. When $tau$ is additive, we give a general construction of $r$-regular CPPs for any positive integer $r$. When $tau$ is not additive, we give many examples of regular CPPs over the extension fields for $r=3,4,5,6,7$ and for arbitrary odd positive integer $r$. These examples are the generalization of the first class of $r$-regular CPPs constructed by Xu, Zeng and Zhang (Des. Codes Cryptogr. 90, 545-575 (2022))." @default.
- W4313197166 created "2023-01-06" @default.
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- W4313197166 date "2022-12-25" @default.
- W4313197166 modified "2023-09-27" @default.
- W4313197166 title "A general construction of regular complete permutation polynomials" @default.
- W4313197166 doi "https://doi.org/10.48550/arxiv.2212.12869" @default.
- W4313197166 hasPublicationYear "2022" @default.
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