TY - JOUR
T1 - On the distribution of orbits of PGL2(q) in Fqn and the Klapper conjecture
AU - Shparlinski, Igor E.
N1 - 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/
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=77950845574&partnerID=8YFLogxK
U2 - 10.1137/090770746
DO - 10.1137/090770746
M3 - Article
AN - SCOPUS:77950845574
SN - 0895-4801
VL - 23
SP - 2093
EP - 2099
JO - SIAM Journal on Discrete Mathematics
JF - SIAM Journal on Discrete Mathematics
IS - 4
ER -