Group Divisible Codes and Their Application in the Construction of Optimal Constant-Composition Codes of Weight Three
Copyright policy )Group Divisible Codes and Their Application in the Construction of Optimal Constant-Composition Codes of Weight Three
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.
13 pages, 1 figure, 4 tables
- Nanyang Technological University Singapore
- Zhejiang Ocean University China (People's Republic of)
- University of Vermont United States
FOS: Computer and information sciences, Discrete Mathematics (cs.DM), Computer Science - Information Theory, Information Theory (cs.IT), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), :Science::Mathematics::Discrete mathematics::Combinatorics [DRNTU], Computer Science - Discrete Mathematics
FOS: Computer and information sciences, Discrete Mathematics (cs.DM), Computer Science - Information Theory, Information Theory (cs.IT), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), :Science::Mathematics::Discrete mathematics::Combinatorics [DRNTU], Computer Science - Discrete Mathematics
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