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

Igor E. Shparlinski

Research output: Contribution to journalArticlepeer-review

27 Downloads (Pure)

Abstract

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
Volume23
Issue number4
DOIs
Publication statusPublished - 2009

Bibliographical note

Copyright SIAM Publications. Article archived for private and non-commercial use with the permission of the author and according to publisher conditions. For further information see http://www.siam.org/

Fingerprint

Dive into the research topics of 'On the distribution of orbits of PGL2(q) in Fqn and the Klapper conjecture'. Together they form a unique fingerprint.

Cite this