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The PBD-Closure of Constant-Composition Codes
Yeow Meng Chee; Ling, A.C.H.; San Ling; Hao Shen;
Information Theory, IEEE Transactions on
Volume 53,
Issue 8,
Aug. 2007
Page(s):2685
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2692
Abstract:
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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