Expansion and linear complexity of the coordinate sequences over Galois rings

The coordinate sequences of the trace sequences over a Galois ring defined by the trace function are used significantly in cryptography, coding and communication applications. In this paper, a p-adic expansion for the coordinate sequences in terms of elementary symmetric functions is provided for the case that the characteristic p of the residue field of the Galois ring is an arbitrary prime, which generalizes the related result of Kumar and Helleseth for the characteristic being p=2. From the expression, upper and lower bounds on the linear complexity of the coordinate sequences are derived.