Quaternary Constant-Composition Codes With Weight 4 and Distances 5 or 6

The sizes of optimal constant-composition codes (CCCs) of weight 3 have been determined by Chee, Ge, and Ling with four cases in doubt. Group divisible codes (GDCs) played an important role in their constructions. In this paper, we study the problem of constructing optimal quaternary CCCs with Hamming weight 4 and minimum distances 5 or 6 through GDCs and Room square approaches. The problem is solved leaving only five lengths undetermined. Previously, the results on the sizes of such quaternary CCCs were scarce.

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