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 fa...

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Bibliographic Details
Published in:IEEE transactions on information theory 2007-08, Vol.53 (8), p.2685-2692
Main Authors: Yeow Meng Chee, Ling, A.C.H., San Ling, Hao Shen
Format: Article
Language:English
Subjects:
Applied sciences
Balancing
Binary codes
Codes
Coding, codes
Computer science
Constant-composition codes
Data transmission
Design
DNA
Educational programs
Exact sciences and technology
Feedback
group divisible designs
Hamming distance
Information theory
Information, signal and communications theory
Memoryless systems
Modulation coding
Optimization
pairwise balanced designs (PBD)
PBD-closure
Research and development
Signal and communications theory
Spread spectrum communication
Telecommunications and information theory
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Summary: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.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2007.901175