Abstract
Ahlswede, Khachatrian, Mauduit and Sárközy introduced the notion of family complexity, Gyarmati, Mauduit and Sárközy introduced the cross-correlation measure for families of binary sequences. It is a challenging problem to find families of binary sequences with both small cross-correlation measure and large family complexity. In this paper we present a family of binary sequences with both small cross-correlation measure and large family complexity by using the properties of character sums and primitive normal elements in finite fields.
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