In this paper new binary sequence families $\mathcal{F}^k$ of period $2^n-1$are constructed for even $n$ and any $k$ with ${\rm gcd}(k,n)=2$ if $n/2$ isodd or ${\rm gcd}(k,n)=1$ if $n/2$ is even. The distribution of theircorrelation values is completely determined. These families have maximumcorrelation $2^{n/2+1}+1$ 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 construction of the large set ofKasami sequences which is exactly the $\mathcal{F}^{k}$ with $k=n/2+1$ isgeneralized.
展开▼
机译：在本文中，对于偶数$ n $和任何$ {$ rm gcd}（k，n）= 2的$ k $，构造了周期为$ 2 ^ n-1 $的新二进制序列族$ \ mathcal {F} ^ k $如果$ n / 2 $是奇数，则$；如果$ n / 2 $是偶数，则$ {\ rm gcd}（k，n）= 1 $。它们的相关值的分布是完全确定的。这些家庭的最大相关性为$ 2 ^ {n / 2 + 1} + 1 $，家庭规模为$ 2 ^ {3n / 2} + 2 ^ {n / 2} $（奇数$ n / 2 $或$ 2 ^ {3n / 2}） + 2 ^ {n / 2} -1 $甚至$ n / 2 $。归纳出Kasami序列的大集合的构造，正是Kasami序列的正好是$ \ mathcal {F} ^ {k} $，其中$ k = n / 2 + 1 $。
展开▼
