Expansion and linear complexity of the coordinate sequences over Galois rings

Authors:
Nigang Sun;Lei Hu
Affiliations:
State Key Laboratory of Information Security, Graduate School of Chinese Academy of Sciences, Beijing 100049, PR China;State Key Laboratory of Information Security, Graduate School of Chinese Academy of Sciences, Beijing 100049, PR China
Venue:
Journal of Complexity
Year:
2006

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Abstract

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.