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.