Bijections Between Group Rings Preserving Character Sums

Authors:
Mariko Hagita;Bernhard Schmidt
Affiliations:
Department of Mathematics, Keio University, Yokohama 223-8522, Japanhagita@comb.math.keio.ac.jp;Universität Augsburg, Universitätsstraße 14, 86135 Augsburg, Germanyschmidt@math.uni-augsburg.de
Venue:
Designs, Codes and Cryptography
Year:
2001

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Abstract

Generalizing an idea in [13], we exhibit some, in general nonhomomorphic, bijections between finite groups which preserve the absolute value of character sums. As a consequence, the existence of a single difference set, relative difference set, building set etc. in certain groups implies the existence of such objects in many other groups.