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The d-ary Sidel'nikov sequence S = s0, s1 … of period q - 1 for a prime power q = pm is a frequently analyzed sequence in the literature. Recently, it turned out that the linear complexity over Fp of the d-ary Sidel'nikov sequence is considerably smaller than the period if the sequence element s( q - 1) /2 mod (q - 1) is chosen adequately. In this paper this work is continued and tight lower bounds on the linear complexity over Fp 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 Fp of the d-ary Sidel'nikov sequence are presented. [ABSTRACT FROM AUTHOR]

The k-error linear complexity of a periodic binary sequence Is defined to be the smallest linear complexity that can be obtained by changing it or fewer bits per period. This contribution focuses on the case of 2n -periodic binary sequences. For it = 1,2, the exact formula for the expected k-error linear complexity of a sequence having maximal possible linear complexity 2n, and the exact formula of the expected 1-error linear complexity of a random 2n-periodic binary sequence are provided. For it k ≥ 2, lowerand upper bounds on the expected value of the k-error linear complexity of a random 2n-periodic binary sequence are established. [ABSTRACT FROM AUTHOR]