On the Linear Complexity and $k$ -Error Linear Complexity Over $ {\BBF }_{p}$ of the $d$-ary Sidel'nikov Sequence

The d-ary Sidel'nikov sequence S = s
₀
, s
₁
... 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.