A Pair of Disjoint 3-GDDs of type g^t u^1
Yanxun Chang, Yeow Meng Chee, Junling Zhou
TL;DR
This paper proves the existence of a pair of disjoint 3-group divisible designs of a specific type, which are useful for constructing optimal constant-weight codes, by showing that necessary conditions are also sufficient.
Contribution
It establishes that the necessary conditions for the existence of such disjoint 3-GDDs are also sufficient, filling a gap in combinatorial design theory.
Findings
Necessary and sufficient conditions for the existence of disjoint 3-GDDs of type g^t u^1.
Construction methods for these designs.
Implications for optimal constant-weight code design.
Abstract
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.
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