18 research outputs found
Group divisible designs with block size 4 and group sizes 4 and 7
In this paper, we consider the existence of group divisible designs (GDDs)
with block size and group sizes and . We show that there exists a
4-GDD of type for all but a finite specified set of feasible values
for .Comment: arXiv admin note: substantial text overlap with arXiv:2109.1122
Spectrum of Sizes for Perfect Deletion-Correcting Codes
One peculiarity with deletion-correcting codes is that perfect
-deletion-correcting codes of the same length over the same alphabet can
have different numbers of codewords, because the balls of radius with
respect to the Levenshte\u{\i}n distance may be of different sizes. There is
interest, therefore, in determining all possible sizes of a perfect
-deletion-correcting code, given the length and the alphabet size~.
In this paper, we determine completely the spectrum of possible sizes for
perfect -ary 1-deletion-correcting codes of length three for all , and
perfect -ary 2-deletion-correcting codes of length four for almost all ,
leaving only a small finite number of cases in doubt.Comment: 23 page
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Designs for graphs with six vertices and nine edges
The design spectrum has been determined for eleven of the 21 graphs with six vertices and nine edges. In this paper we completely solve the design spectrum problem for the remaining ten graphs