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Group Divisible Codes and Their Application in the Construction of Optimal Constant-Composition Codes of Weight Three

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3 Author(s)
Yeow Meng Chee ; Sch. of Phys. & Math. Sci., Nanyang Technol. Univ., Singapore ; Gennian Ge ; Alan C. H. Ling

The concept of group divisible codes, a generalization of group divisible designs with constant block size, is introduced in this paper. This new class of codes is shown to be useful in recursive constructions for constant-weight and constant-composition codes. Large classes of group divisible codes are constructed which enabled the determination of the sizes of optimal constant-composition codes of weight three (and specified distance), leaving only four cases undetermined. Previously, the sizes of constant-composition codes of weight three were known only for those of sufficiently large length.

Published in:

IEEE Transactions on Information Theory  (Volume:54 ,  Issue: 8 )