Addendum to Sidel'nikov sequences over nonprime fields

Official URL: http://dx.doi.org/10.1016/j.ipl.2013.02.008

Sidel'nikov sequences over nonprime fields $\F_{p^t}$ of characteristic $p$ were introduced by Brandst\"atter and Meidl in 2008. It was shown that under certain conditions this sequence construction exhibits a large linear complexity if one chooses the basis $\mathcal{B}= \{\beta_0, \beta_1,\ldots, \beta_{t-1}\}$ of $\F_{p^t}$ such that ${\rm Tr}(\beta_j) = 0$ for $1 \le j \le t-1$ and ${\rm Tr}(\beta_0) = 1$. In this paper we use dual bases to show that this result holds for Sidel'nikov sequences over nonprime fields independently from the choice of the basis. Moreover with a more straightforward argumentation we are able to relax the conditions for the lower bound on the linear complexity.