Group divisible codes and their application in the construction of optimal constant-composition codes of weight three

• Main Authors: Ling, Alan C. H., Chee, Yeow Meng, Ge, Gennian
• Format: Article
• Language: English
• Published: 2009
• Subjects: DRNTU::Science::Mathematics::Discrete mathematics::Combinatorics
• Online Access: https://hdl.handle.net/10356/92225; http://hdl.handle.net/10220/6042; http://sfxna09.hosted.exlibrisgroup.com:3410/ntu/sfxlcl3?sid=metalib:EBSCO_APH&id=doi:&genre=&isbn=&issn=00189448&date=2008&volume=54&issue=8&spage=3552&epage=3564&aulast=Yeow&aufirst=Meng%20Chee&auinit=&title=IEEE%20Transactions%20on%20Information%20Theory&atitle=Group%20Divisible%20Codes%20and%20Their%20Application%20in%20the%20Construction%20of%20Optimal%20Constant%2DComposition%20Codes%20of%20Weight%20Three%2E
• Institution: Nanyang Technological University

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.