Generalized Kasami Sequences: The Large Set

In this correspondence, new binary sequence families F
^k
of period 2
ⁿ
-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
^n/2+1
and family size 2
^3n/2
+ 2
^n/2
for odd n/2 or 2
^3n/2
+2
^n/2
-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.