On the $k$-error linear complexity of subsequences of $d$-ary Sidel'nikov sequences over prime field ${\mathbb{F}}_d$

We study the $k$-error linear complexity of subsequences of the $d$-ary Sidel’nikov sequences over the prime field ${\mathbb{F}}_d$. A general lower bound for the $k$-error linear complexity is given. For several special periods, we show that these sequences have large $k$-error linear complexity.