On the arithmetic autocorrelation of the Legendre sequence

Richard Hofer; Arne Winterhof

doi:10.3934/amc.2017015

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2017, Volume 11, Issue 1: 237-244. Doi: 10.3934/amc.2017015

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On the arithmetic autocorrelation of the Legendre sequence

Richard Hofer^, and
Arne Winterhof

Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenberger Str. 69,4040 Linz, Austria

^* Corresponding author
^* Corresponding author

Received: September 30, 2015

Revised: January 31, 2016

Published: May 2017

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Abstract

The Legendre sequence possesses several desirable features of pseudorandomness in view of different applications such as a high linear complexity (profile) for cryptography and a small (aperiodic) autocorrelation for radar, gps, or sonar. Here we prove the first nontrivial bound on its arithmetic autocorrelation, another figure of merit introduced by Mandelbaum for errorcorrecting codes.

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Mathematics Subject Classification: Primary: 94A55; Secondary: 11T71, 94A05, 94A60.

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References

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