On the Linear Complexity and $k$ -Error Linear Complexity Over ${BBF }_{p}$ of

The d-ary Sidel´nikov sequence S = s₀, s₁... of period q-1 for a prime power q=p^m is a frequently analyzed sequence in the literature. Recently, it turned out that the linear complexity over F_p of the d-ary Sidel´nikov sequence is considerably smaller than the period if the sequence element s_{(q-1)/2mod(q-1)} is chosen adequately. In this paper this work is continued and tight lower bounds on the linear complexity over F_p of the d-ary Sidel´nikov sequence are given. For certain cases exact values are provided. Finally, results on the k-error linear complexity over F_p of the d-ary Sidel´nikov sequence are presented.