6 research outputs found

    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

    Universal Cycles for Minimum Coverings of Pairs by Triples, with Application to 2-Radius Sequences

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    A new ordering, extending the notion of universal cycles of Chung {\em et al.} (1992), is proposed for the blocks of kk-uniform set systems. Existence of minimum coverings of pairs by triples that possess such an ordering is established for all orders. Application to the construction of short 2-radius sequences is given, with some new 2-radius sequences found through computer search.Comment: 18 pages, to appear in Mathematics of Computatio

    Spectrum of Sizes for Perfect Deletion-Correcting Codes

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    One peculiarity with deletion-correcting codes is that perfect tt-deletion-correcting codes of the same length over the same alphabet can have different numbers of codewords, because the balls of radius tt 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 tt-deletion-correcting code, given the length nn and the alphabet size~qq. In this paper, we determine completely the spectrum of possible sizes for perfect qq-ary 1-deletion-correcting codes of length three for all qq, and perfect qq-ary 2-deletion-correcting codes of length four for almost all qq, leaving only a small finite number of cases in doubt.Comment: 23 page

    The α\alpha-Arboricity of Complete Uniform Hypergraphs

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    International audienceα\alpha-Acyclicity is an important notion in database theory. The α\alpha-arboricity of a hypergraph H is the minimum number of α\alpha-acyclic hypergraphs that partition the edge set of H. The α\alpha-arboricity of the complete 3-uniform hypergraph is determined completely
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