On $k$-error linear complexity of pseudorandom binary sequences derived from Euler quotients

We investigate the k-error linear complexity of pseudorandom binary sequences of period pr derived from the Euler quotients modulo pr−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 pr) does not decrease dramatically for k < pr−2(p− 1)2/2.