On Niho type cross-correlation functions of m-sequences

Authors:
Tor Helleseth;Jyrki Lahtonen;Petri Rosendahl
Affiliations:
Department of Informatics, University of Bergen, N-5020 Bergen, Norway;Department of Mathematics, University of Turku, F-20014 Turku, Finland;Department of Mathematics, University of Turku, F-20014 Turku, Finland
Venue:
Finite Fields and Their Applications
Year:
2007

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Abstract

Assume that d=1(modq-1). We study the number of solutions to (x+1)^d=x^d+1 in GF(q^2). In addition, we give a simple proof of the fact that the cross-correlation function between two m-sequences, which differ by a decimation of this type, is at least four-valued.