The PBD-closure of constant-composition codes

• Main Authors: Ling, Alan C. H., Chee, Yeow Meng, Ling, San, Shen, Hao
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2009
• Subjects: DRNTU::Science::Mathematics::Discrete mathematics::Combinatorics
• Online Access: https://hdl.handle.net/10356/91732; http://hdl.handle.net/10220/6036; http://sfxna09.hosted.exlibrisgroup.com:3410/ntu/sfxlcl3?sid=metalib:EBSCO_APH&id=doi:&genre=&isbn=&issn=00189448&date=2007&volume=53&issue=8&spage=2685&epage=2692&aulast=Yeow&aufirst=Meng%20Chee&auinit=&title=IEEE%20Transactions%20on%20Information%20Theory&atitle=The%20PBD%2DClosure%20of%20Constant%2DComposition%20Codes%2E
• Institution: Nanyang Technological University

We show an interesting pairwise balanced design (PBD)-closure result for the set of lengths of constant-composition codes whose distance and size meet certain conditions. A consequence of this PBD-closure result is that the size of optimal constant-composition codes can be determined for infinite families of parameter sets from just a single example of an optimal code. As an application, the sizes of several infinite families of optimal constant-composition codes are derived. In particular, the problem of determining the size of optimal constant-composition codes having distance four and weight three is solved for all lengths sufficiently large. This problem was previously unresolved for odd lengths, except for lengths seven and eleven.