In this correspondence, new binary sequence families ${cal F}^{k}$ of period $2^{n}-1$ are constructed for even $n$ and any $k$ with ${rm gcd}(k,n)=2$ if $n/2$ is odd or ${rm gcd}(k,n)=1$ if $n/2$ is even. The distribution of their correlation values is completely determined. These families have maximum correlation $2^{n/2+1}+1$ 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 $k=n/2+1$.
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机译：在这种对应关系中，为偶数$ n $和任何带有$ {rm gcd}（k，n的$ k $）构造了周期为$ 2 ^ {n} -1 $的新二进制序列族$ {cal F} ^ {k} $ ）= 2 $（如果$ n / 2 $是奇数），或者$ {rm gcd}（k，n）= 1 $（如果$ n / 2 $是偶数）。它们的相关值的分布是完全确定的。这些家庭的最大相关度为$ 2 ^ {n / 2 + 1} + 1 $，家庭规模为$ 2 ^ {3n / 2} + 2 ^ {n / 2} $（奇数为$ n / 2 $或$ 2 ^ {3n / 2） } + 2 ^ {n / 2} -1 $甚至$ n / 2 $。建议的族包括Kasami序列的大集合，其中$ k $被视为$ k = n / 2 + 1 $。
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