On the cycle structure of permutation polynomials

Authors:
AyçA ÇEşMelioğLu;Wilfried Meidl;Alev TopuzoğLu
Affiliations:
Sabancı University, MDBF, Orhanlı, 34956 Tuzla, İstanbul, Turkey;Sabancı University, MDBF, Orhanlı, 34956 Tuzla, İstanbul, Turkey;Sabancı University, MDBF, Orhanlı, 34956 Tuzla, İstanbul, Turkey
Venue:
Finite Fields and Their Applications
Year:
2008

Citing 3
Cited 3

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Abstract

Any permutation of a finite field F"q can be represented by a polynomial P"n(x)=(...+((a"0x+a"1)^q^-^2+a"2)^q^-^2+...+a"n)^q^-^2+a"n"+"1, for some n=0. P"0 is linear and the cycle structure of P"1 is known. In this work we present the cycle structure of the polynomials P"2(x) and P"3(x) completely and give methods for constructing P"n(x) with full cycle, for arbitrary n=1.