On $k$-error linear complexity of pseudorandom binary sequences derived from Euler quotients
Zhixiong Chen, Vladimir Edemskiy, Pinhui Ke, Chenhuang Wu · Advances in Mathematics of Communications · 2018
We investigate the $ k$-error linear complexity of pseudorandom binary sequences of period $ p^{\mathfrak{r}} $ derived from the Euler quotients modulo $ p^{\mathfrak{r}-1} $, a power of an odd prime $ p $ for $ \mathfrak{r}≥2 $. When $ \mathfrak{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 $ \mathfrak{r}≥3 $. We also state the exact values of the $ k $-error linear complexity for the case of $ \mathfrak{r} = 3 $. From the results, we can find that the $ k $-error linear complexity of the sequences (of period $ p^{\mathfrak{r}} $) does not decrease dramatically for $ k