The PBD-Closure of Constant-Composition Codes
Information Theory
2007-12-18 v1 Discrete Mathematics
Combinatorics
math.IT
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.
Cite
@article{arxiv.0712.2552,
title = {The PBD-Closure of Constant-Composition Codes},
author = {Yeow Meng Chee and Alan C. H. Ling and San Ling and Hao Shen},
journal= {arXiv preprint arXiv:0712.2552},
year = {2007}
}
Comments
8 pages