Trace Representation of Binary Generalized Cyclotomic Sequences with Length p^m

Abstract

Some new generalized cyclotomic sequences defined by C. Ding and T. Helleseth are proven to exhibit a number of good randomness properties. In this paper, we determine the defining pairs of these sequences of length p^m (p prime, m å 2) with order two, then from which we obtain their trace representation. Thus their linear complexity can be derived using Key's method.