On linear complexity of sequences over GF(2n)

Authors:
A. M. Youssef;G. Gong
Affiliations:
Concordia Institute for Information Systems Engineering, Concordia University, Montreal, Que., Canada;Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, Ont., Canada
Venue:
Theoretical Computer Science
Year:
2006

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Abstract

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 over GF(2n) but given in their binary representation. Let a = {ai} be a sequence over GF(2n). Then ai can be represented by ai =Σj=0n-1 aijαj,aij ∈ GF(2), 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. bi = Σj=0r-1 aijγj, We study the relation between the minimal polynomial of a and b.