Permutation Quadrinomials over Finite Fields with cycle type $1+4+4+\cdots +4$

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2025年9月25日

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B. Kevinsam,
S. Radha,
P. Vanchinathan

摘要

In all finite fields where the order of the multiplicative group is a multiple of 4, we construct permutations that are compositions of disjoint four-cycles on the multiplicative group, which, as polynomials have four terms. For a single field we are able to construct $3(q-1)/2$ $3 (q - 1) / 2$ permutation polynomials explicitly providing formulas for their coefficients, all having the same cycle type. As an illustration a table of 60 such quadrinomials for $\textbf{F}_{41}$ $F_{41}$ is provided in an appendix.

Permutation Quadrinomials over Finite Fields with cycle type \(1+4+4+\cdots +4\)

摘要