We propose a computation method for linear complexity of series of generalized cyclotomic sequences with period p n+1 . This method is based on using the polynomial of the classic cyclotomic sequences of period p. We found the linear complexity of generalized cyclotomic sequences corresponding to the classes of biquadratic residues and Hall sequences.

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We investigate the k-error linear complexity of pseudorandom binary sequences of period p r derived from the Euler quotients modulo p r−1 , a power of an odd prime p for r ≥ 2. When r = 2, this is just the case of polynomial quotients (including Fermat quotients) modulo p, which has been studied in an earlier work of Chen, Niu and Wu. In this work, we establish a recursive relation on the k-error linear complexity of the sequences for the case of r ≥ 3. We also state the exact values of the k-error linear complexity for the case of r = 3. From the results, we can find that the k-error linear complexity of the sequences (of period p r ) does not decrease dramatically for k < p r−2 (p − 1) 2 /2.

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