Linear complexity over Fp and trace representation of Lempel-Cohn-Eastman sequences

In this correspondence, the linear complexity over of Lempel–Cohn–Eastman (LCE) sequences of period 1 for an odd prime is determined. For = 3 5 and 7, the exact closed-form expressions for the linear complexity over of LCE sequences of period 1 are derived. Further, the trace representations for LCE sequences of period 1 for = 3 and 5 are found by computing the values of all Fourier coefficients in for the sequences.