2,807 research outputs found

    Group Divisible Codes and Their Application in the Construction of Optimal Constant-Composition Codes of Weight Three

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    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

    A Pair of Disjoint 3-GDDs of type g^t u^1

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    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 gtu1g^t u^1 and establish that its necessary conditions are also sufficient.Comment: Designs, Codes and Cryptography (to appear
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