On linear complexity of sequences over GF(2n)

In this paper, we consider some aspects related to determining the linear complexity of sequences over GF(2n). 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 overGF(2n) but given in their binary representation. Let a={ai} be a sequence overGF(2n). Then ai can be represented by ai = ∑n−1 j=0 aij j , aij ∈ GF(2), where 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 { 0, 1, . . . , n−1}), i.e., bi = ∑r−1 j=0 aij j . We study the relation between the minimal polynomial of a and b. © 2006 Elsevier B.V. All rights reserved.