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

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