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arXiv · 0807.2680

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

Yeow Meng Chee·Gennian Ge·Alan C. H. Ling
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Abstract

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.

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Yeow Meng Chee, Gennian Ge, Alan C. H. Ling. 2008-07-17. Group Divisible Codes and Their Application in the Construction of Optimal Constant-Composition Codes of Weight Three. https://doi.org/10.1109/tit.2008.926349

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