English

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

Information Theory 2008-07-18 v1 Discrete Mathematics Combinatorics math.IT

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.

Keywords

Cite

@article{arxiv.0807.2680,
  title  = {Group Divisible Codes and Their Application in the Construction of Optimal Constant-Composition Codes of Weight Three},
  author = {Yeow Meng Chee and Gennian Ge and Alan C. H. Ling},
  journal= {arXiv preprint arXiv:0807.2680},
  year   = {2008}
}

Comments

13 pages, 1 figure, 4 tables

R2 v1 2026-06-21T11:01:29.224Z