Generalized Kasami Sequences: The Large Set

In this correspondence, new binary sequence families F<sup>k</sup> of period 2<sup>n</sup>-1 are constructed for even n and any k with gcd(k,n)=2 if n/2 is odd or gcd(k,n)=1 if n/2 is even. The distribution of their correlation values is completely determined. These families have maximum correlation 2<sup>n/2+1</sup> and family size 2<sup>3n/2</sup> + 2<sup>n/2</sup> for odd n/2 or 2<sup>3n/2</sup>+2<sup>n/2</sup>-1 for even n/2. The proposed families include the large set of Kasami sequences, where the k is taken as k=n/2+1.

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