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\(A_m\)-permutation polynomials. (English) Zbl 1103.11036

The author presents a class of polynomials which induce a permutation polynomial on the set of polynomials of degree less than a prescribed bound over a finite field. Three criteria are given to characterize such polynomials. The paper concludes with an example to illustrate the process.

MSC:

11T06 Polynomials over finite fields
11T55 Arithmetic theory of polynomial rings over finite fields
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References:

[1] Goss, Basic structures of function field arithmetic (1996) · Zbl 0874.11004 · doi:10.1007/978-3-642-61480-4
[2] DOI: 10.2307/1967217 · JFM 28.0135.03 · doi:10.2307/1967217
[3] DOI: 10.2307/2321681 · Zbl 0406.12011 · doi:10.2307/2321681
[4] DOI: 10.1215/S0012-7094-40-00639-1 · Zbl 0026.05304 · doi:10.1215/S0012-7094-40-00639-1
[5] Hermite, C.R. Acad. Sci. Paris 57 pp 750– (1863)
[6] Lidl, Finite fields 20 (1983)
[7] Lidl, Acta Arith. 22 pp 257– (1972)
[8] DOI: 10.1080/0161-117791832814 · doi:10.1080/0161-117791832814
[9] Schmidt, Equations over finite fields–an elementary approach 536 (1976) · Zbl 0329.12001 · doi:10.1007/BFb0080437
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