Zero-difference balanced (ZDB) functions, which have many applications in coding theory and sequence design, have received a lot of attention in recent years. In this letter, based on two known classes of ZDB functions, a new class of ZDB functions, which is defined on the group (Z2e-1×Zn,+) is presented, where e is a prime and n=p1m1p2m2…pkmk, pi is odd prime satisfying that e|(pi-1) for any 1≤i≤k . In the case of gcd(2e-1,n)=1, the new constructed ZDB functions are cyclic.

Constant composition codes (CCCs) are a special class of constant-weight codes. They include permutation codes as a subclass. The study and constructions of CCCs with parameters meeting certain bounds have been an interesting research subject in coding theory. A bridge from zero difference balanced (ZDB) functions to CCCs with parameters meeting the Luo-Fu-Vinck-Chen bound has been established by Ding (IEEE Trans. Information Theory 54(12) (2008) 5766-5770). This provides a new approach for obtaining optimal CCCs. The objective of this letter is to construct two classes of ZDB functions whose parameters not covered in the literature, and then obtain two classes of optimal CCCs meeting the Luo-Fu-Vinck-Chen bound from these new ZDB functions.

Constant weight codes have mathematical interest and practical applications such as coding for bandwidth-efficient channels and construction of spherical codes for modulation. In this letter, by using difference balanced functions with d-form property, we constructed a class of constant composition code with new parameters, which achieves the equal sign of generalized Johnson bound.

In this paper, we present two classes of zero difference balanced (ZDB) functions, which are derived by difference balanced functions, and a class of perfect ternary sequences respectively. The proposed functions have parameters not covered in the literature, and can be used to design optimal constant composition codes, and perfect difference systems of sets.