Quantum Period Reconstruction of Binary Sequences

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.

• Type: Conference
• Year: 2006
• Where: AAECC
• Authors: Florina Piroi, Arne Winterhof
• Keywords: AAECC 2006, Algorithms, Binary Sequence, Small Autocorrelation, Time Quantum Algorithm