The PBD-Closure of Constant-Composition Codes

Authors :: Chee, Yeow Meng
Ling, Alan C. H.
Ling, San
Shen, Hao
Source :: IEEE Transactions on Information Theory, vol. 53, No. 8, August 2007, pp. 2685-2692
Publication Year :: 2007
Abstract: We show an interesting 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 size 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.<br />Comment: 8 pages

Subjects :: Computer Science - Information Theory
Computer Science - Discrete Mathematics
Mathematics - Combinatorics

Database :: arXiv
Journal :: IEEE Transactions on Information Theory, vol. 53, No. 8, August 2007, pp. 2685-2692
Publication Type :: Report
Accession number :: edsarx.0712.2552
Document Type :: Working Paper
Full Text :: https://doi.org/10.1109/TIT.2007.901175