Properties of the error linear complexity spectrum

Authors:
Tuvi Etzion;Nicholas Kalouptsidis;Nicholas Kolokotronis;Konstantinos Limniotis;Kenneth G. Paterson
Affiliations:
Department of Computer Science, Technion-Israel Institute of Technology, Haifa, Israel;Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Athens, Greece;Department of Computer Science and Technology, University of Peloponnese, Tripolis, Greece;Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Athens, Greece;Information Security Group, Royal Holloway, University of London, Egham, Surrey, UK
Venue:
IEEE Transactions on Information Theory
Year:
2009

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Abstract

This paper studies the error linear complexity spectrum of binary sequences with period 2n. A precise categorization of those sequences having two distinct critical points in their spectra, as well as an enumeration of these sequences, is given. An upper bound on the maximum number of distinct critical points that the spectrum of a sequence can have is proved, and a construction which yields a lower bound on this number is given. In the process simpler proofs of some known results on the linear complexity and k-error linear complexity of sequences with period 2n are provided.