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The PBD-Closure of Constant-Composition Codes

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4 Author(s)
Yeow Meng Chee ; Nanyang Technol. Univ., Singapore ; Ling, A.C.H. ; San Ling ; Hao Shen

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.

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Information Theory, IEEE Transactions on  (Volume:53 ,  Issue: 8 )