On the linear complexity and k -error linear complexity over \BBF p of the d-ary Sidel'nikov Sequence

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Official URL: http://dx.doi.org/10.1109/TIT.2007.909129

The $d$-ary Sidel'nikov sequence $S = s_0, s_1 \ldots$ 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 $s_{(q-1)/2\bmod (q-1)}$ 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.