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arXiv · 0712.2552

The PBD-Closure of Constant-Composition Codes

Yeow Meng Chee·Alan C. H. Ling·San Ling·Hao Shen
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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.

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Yeow Meng Chee, Alan C. H. Ling, San Ling, Hao Shen. 2007-12-16. The PBD-Closure of Constant-Composition Codes. https://doi.org/10.1109/tit.2007.901175

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