Lower bounds on sequence complexity via generalised vandermonde determinants

Authors:
Nicholas Kolokotronis;Konstantinos Limniotis;Nicholas Kalouptsidis
Affiliations:
Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Athens, Greece;Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Athens, Greece;Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Athens, Greece
Venue:
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
Year:
2006

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Abstract

Binary sequences generated by nonlinearly filtering maximal length sequences with period 2n–1 are studied in this paper. We focus on the particular class of equidistant filters and provide improved lower bounds on the linear complexity of the filtered sequences. This is achieved by first considering and proving properties of generalised Vandermonde determinants. Furthermore, it is shown that the methodology developed can be used for studying properties of any nonlinear filter.