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Fermat-Euler quotients arose from the study of the first case of Fermat'sLast Theorem, and have numerous applications in number theory. Recently theywere studied from the cryptographic aspects by constructing many pseudorandombinary sequences, whose linear complexities and trace representations werecalculated. In this work, we further study their correlation measures by usingthe approach based on Dirichlet characters, Ramanujan sums and Gauss sums. Ourresults show that the $4$-order correlation measures of these sequences arevery large. Therefore they may not be suggested for cryptography.

Correlation measures of binary sequences derived from Euler quotients