ISSN:
1573-7586
Keywords:
directed designs
;
directed packings
;
deletion correcting codes
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract The aim of this paper is an investigation of directed t-packings and in particular of directed t-Steiner systems. A new upper bound on the number of points k for directed t-Steiner systems T(t,k,k) is obtained. We disprove a conjecture of Levenshtein on T(t,k,k) for t ≥ 3 by showing that a T(4,6,6) exists. Furthermore, it is proved that the symmetric group S 6 can be partitioned into 30 disjoint T(4,6,6)s. Extensive computer search shows that the tight upper bound on K for t =4,5 is 6 and for t=6 is 7. The non-existence of further small directed t-Steiner systems is established, and large directed t-packings for t,4,5,6 are constructed.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1008353723204
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