On the $k$-error linear complexity of subsequences of $d$-ary Sidelnikov sequences over prime field $mathbb{F}_{d}$

We study the $k$-error linear complexity of subsequences of the $d$-ary Sidelnikov 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.