Addendum to Sidelʼnikov sequences over nonprime fields

Sidelʼnikov sequences over nonprime fields Fpt of characteristic p were introduced by Brandstätter and Meidl in 2008. It was shown that under certain conditions this sequence construction exhibits a large linear complexity if one chooses the basis B={β0,β1,…,βt−1} of Fpt such that Tr(βj)=0 for 1⩽j⩽t−1 and Tr(β0)=1. In this paper we use dual bases to show that this result holds for Sidelʼnikov 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.