Geodesic
From a 1-rotational RBIBD to a partitioned difference family
The electronic journal of combinatorics, Tome 17 (2010)
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Generalizing the case of $\lambda=1$ given by Buratti and Zuanni [Bull Belg. Math. Soc. (1998)], we characterize the $1$-rotational difference families generating a 1-rotational $(v,k,\lambda)$-RBIBD, that is a $(v,k,\lambda)$ resolvable balanced incomplete block design admitting an automorphism group $G$ acting sharply transitively on all but one point $\infty$ and leaving invariant a resolution $\cal R$ of it. When $G$ is transitive on $\cal R$ we prove that removing $\infty$ from a parallel class of $\cal R$ one gets a partitioned difference family, a concept recently introduced by Ding and Yin [IEEE Trans. Inform. Theory, 2005] and used to construct optimal constant composition codes. In this way, by exploiting old and new results about the existence of 1-rotational RBIBDs we are able to derive a great bulk of previously unnoticed partitioned difference families. Among our RBIBDs we construct, in particular, a $(45,5,2)$-RBIBD whose existence was previously in doubt.
DOI : 10.37236/411
Classification : 05B05, 05E18
Mots-clés : 1-rotational RBIBD, 1-rotational difference family, partitioned difference family, constant composition code 
@article{10_37236_411,
     author = {Marco Buratti and Jie Yan and Chengmin Wang},
     title = {From a 1-rotational {RBIBD} to a partitioned difference family},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/411},
     zbl = {1204.05027},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/411/}
}
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Marco Buratti; Jie Yan; Chengmin Wang. From a 1-rotational RBIBD to a partitioned difference family. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/411

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