The Peak to Sidelobe Level of the Most Significant Bit of Trace Codes over Galois Rings

Authors:
Patrick Solé;Dimitrii Zinoviev
Affiliations:
CNRS-I3S, Les Algorithmes, Euclide B, 2000, Sophia Antipolis, France 06 903;CNRS-I3S, Les Algorithmes, Euclide B, 2000, Sophia Antipolis, France 06 903
Venue:
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Year:
2008

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Abstract

Weighted degree trace codes over even characteristic Galois rings give binary sequences by projection on their most significant bit (MSB). Upper bounds on the aperiodic correlation, peak to sidelobe level (PSL), partial period imbalance and partial period pattern imbalance of these sequences are derived. The proof technique involves estimates of incomplete character sums over Galois rings, combining Weil-like bounds with Fourier transform estimates.