Addendum to Sidel'nikov sequences over nonprime fields

摘要

Sidel'nikov sequences over nonprime fields Fpt of characteristic p were introduced by Brandstaetter 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 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;