Optimal Ternary Constant-Composition Codes of Weight Four and Distance Five

Constant-composition codes (CCCs) are a generalization of constant weight codes and permutation codes. The concept of group divisible codes, an analog of group divisible designs in combinatorial design theory, was first introduced by Chee et al. This new class of codes has been shown to be useful in recursive constructions of constant-weight codes and constant-composition codes. In this paper, we consider the problem of determining the maximal sizes of ternary constant-composition codes of weight four and distance five using group divisible codes as the main tools. We determine the exact values for these parameters. The previously known results are those with code length no greater than 10.