On the arithmetic autocorrelation of the Legendre sequence
Richard Hofer, Arne Winterhof · Advances in Mathematics of Communications · 2017
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.