Quantum period reconstruction of binary sequences

Authors:
Florina Piroi;Arne Winterhof
Affiliations:
Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Linz, Austria;Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Linz, Austria
Venue:
AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Year:
2006

Citing 8
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Abstract

We consider the problem of determining the period of a binary sequence. For sequences with small autocorrelation we prove the existence of a polynomial time quantum algorithm for the above problem based on an algorithm of Hales and Hallgren. We apply this result to several concrete examples for which the autocorrelation can be estimated using known bounds on character sums.