On the distribution of orbits of PGL2(q) in Fqn and the Klapper conjecture

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Motivated by a conjecture of Klapper [Finite Fields, Coding Theory, and Advances in Communications and Computing, Marcel Dekker, New York, 1993], we study the distribution of elements ζ of a finite field F of qn elements under the action of the transformations ? -· (aζ + b)/(cζ + d) for matrices ( acbd) ε PGL2(q). We slightly improve a result of Niederreiter and Winterhof [Finite Fields Appl, 9 (2003), pp. 458-471] towards this conjecture. On the other hand, we also show that the original conjecture is false as stated.

Original languageEnglish
Pages (from-to)2093-2099
Number of pages7
JournalSIAM Journal on Discrete Mathematics
Issue number4
Publication statusPublished - 2009

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