On the complexity of a family related to the Legendre symbol

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.