The PBD-Closure of Constant-Composition Codes

—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 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.

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Yeow Meng Chee, Alan C. H. Ling, San Ling, Hao Shen
• Keywords: Constant-composition Codes, CORR 2007, Education, Infinite Families, Optimal Constant-composition Codes