Binary sequence pairs with optimal periodic correlation have important applications in many fields of communication systems. In this letter, four new families of binary sequence pairs are presented based on the generalized cyclotomy over Z5q, where q ≠ 5 is an odd prime. All these binary sequence pairs have optimal three-level correlation values {-1, 3}.

In this letter, several new families of binary sequence pairs with period N=np, where p is a prime and gcd(n,p)=1, and optimal correlation values 1 and -3 are constructed. These classes of binary sequence pairs are based on Chinese remainder theorem. The constructed sequence pairs have optimum balance among 0's and 1's.

A new subfamily of sequences with optimal correlation properties is constructed for the generalized Kasami set. A lower bound on the linear span is established. It is proved that with suitable choices of parameters, this subfamily has exponentially larger linear spans than either No sequences or TN sequences. A class of sequences with ideal autocorrelation is also proved to have large linear span.

In this paper, using p-ary bent functions defined on vector space over the finite field Fpk, we generalized the construction method of the families of p-ary bent sequences with balanced and optimal correlation properties introduced by Kumar and Moreno for an odd prime p, called generalized p-ary bent sequences. It turns out that the family of balanced p-ary sequences with optimal correlation property introduced by Moriuchi and Imamura is a special case of the newly constructed generalized p-ary bent sequences.