On the Linear Complexity and $k$-Error Linear Complexity Over $ {\BBF }_{p}$ of the $d$-ary Sidel'nikov Sequence
Hassan Aly, Wilfried Meidl · IEEE Transactions on Information Theory · 2007
The d-ary Sidel'nikov sequence S = s0, s1... of period q-1 for a prime power q=pmis a frequently analyzed sequence in the literature. Recently, it turned out that the linear complexity over Fpof 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 Fpof the d-ary Sidel'nikov sequence are given. For certain cases exact values are provided. Finally, results on the k-error linear complexity over Fpof the d-ary Sidel'nikov sequence are presented.