On linear complexity of sequences over

In this paper, we consider some aspects related to determining the linear complexity of sequences over . In particular, we study the effect of changing the finite field basis on the minimal polynomials, and thus on the linear complexity, of sequences defined over but given in their binary representation. Let a={ai} be a sequence over . Then ai can be represented by , , where α is the root of the irreducible polynomial defining the field. Consider the sequence b={bi} whose elements are obtained from the same binary representation of a but assuming a different set of basis (say {γ0,γ1,…,γn-1}), i.e., . We study the relation between the minimal polynomial of a and b.