Abstract
Ahlswede, Khachatrian, Mauduit and A. Sárközy introduced the notion of family-complexity of families of binary sequences. They estimated the family-complexity of a large family related to Legendre symbol introduced by Goubin, Mauduit and Sárközy. Here their result is improved, and apart from the constant factor the best lower bound is given for the family-complexity.
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References
R. Ahlswede, L.H. Khachatrian, C. Mauduit and A. Sárközy, A complexity measure for families of binary sequences, Period. Math. Hungar., 46 (2003), 107–118.
L. Goubin, C. Mauduit and A. Sárközy, Construction of large families of pseudorandom binary sequences, J. Number Theory, 106 (2004), 56–69.
A. Weil, Sur les courbes algébriques et les variétés qui sén déduisent, Act. Sci. Ind. 1041, Hermann, Paris, 1948.
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Communicated by Attila Pethő
Research partially supported by Hungarian National Foundation for Scientific Research, Grants No. K67676 and PD72264 and the János Bolyai Research Fellowship.
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Gyarmati, K. On the complexity of a family related to the Legendre symbol. Period Math Hung 58, 209–215 (2009). https://doi.org/10.1007/s10998-009-10209-4
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DOI: https://doi.org/10.1007/s10998-009-10209-4