Combinatorial Constructions of Optimal Constant-Composition Codes

On Generalized Zero-Difference Balanced Functions

“…Furthermore we obtain some constant composition codes and difference systems of sets directly from G-ZDB functions (Section 4), which also generalize the main results in [2,5,6]. …”

“…Moreover, in the same way as that in [2,6], we can construct constant composition codes and difference system of sets directly from G-ZDB functions. Basing on some special G-ZDB functions, we prove that the corresponding CCCs are optimal, and the DSSs constructed by the G-ZDB function f is perfect when f is a ZDB function.…”

“…, w l−1 ]) l constant composition code is optimal when the bound of Lemma 1.2 is achieved. In [2,6], the link between ZDB functions and optimal CCCs is established. Lemma 1.3 ( [2,6]).…”

“…In [2,6], the link between ZDB functions and optimal CCCs is established. Lemma 1.3 ( [2,6]). Suppose that f is an (n, l, λ)-ZDB from an abelian group (A, +) of order n to an abelian group (B, +) of order l, and Im(f ) is the image set of f with |Im(f )| = l. Let A = {a 0 , .…”

“…By (3) of Lemma 2.2, we know that each nonzero 2-cyclotomic coset has exactly m elements. And so by taking p = 2 in the proofs of Theorems 3.1 and 3.2, the corresponding G-ZDB function is just the ZDB function constructed by Ding [2,6], and so one can obtain Theorems 2 and 3 in [5], respectively.…”