14 research outputs found
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
A Pair of Disjoint 3-GDDs of type g^t u^1
Pairwise disjoint 3-GDDs can be used to construct some optimal
constant-weight codes. We study the existence of a pair of disjoint 3-GDDs of
type and establish that its necessary conditions are also sufficient.Comment: Designs, Codes and Cryptography (to appear
Group Divisible Codes and Their Application in the Construction of Optimal Constant-Composition Codes of Weight Three
The concept of group divisible codes, a generalization of group divisible
designs with constant block size, is introduced in this paper. This new class
of codes is shown to be useful in recursive constructions for constant-weight
and constant-composition codes. Large classes of group divisible codes are
constructed which enabled the determination of the sizes of optimal
constant-composition codes of weight three (and specified distance), leaving
only four cases undetermined. Previously, the sizes of constant-composition
codes of weight three were known only for those of sufficiently large length.Comment: 13 pages, 1 figure, 4 table