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Denis S. Krotov 《Discrete Mathematics》2017,340(12):2723-2731
A subspace bitrade of type is a pair of two disjoint nonempty collections of -dimensional subspaces of a -dimensional space over the finite field of order such that every -dimensional subspace of is covered by the same number of subspaces from and . In a previous paper, the minimum cardinality of a subspace bitrade was established. We generalize that result by showing that for admissible , , and , the minimum cardinality of a subspace bitrade does not depend on . An example of a minimum bitrade is represented using generator matrices in the reduced echelon form. For , the uniqueness of a minimum bitrade is proved. 相似文献
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Denis S. Krotov 《Discrete Mathematics》2017,340(10):2559-2572
An extended -perfect trade is a pair of two disjoint binary distance- even-weight codes such that the set of words at distance from coincides with the set of words at distance from . Such trade is called primary if any pair of proper subsets of and is not a trade. Using a computer-aided approach, we classify nonequivalent primary extended -perfect trades of length , constant-weight extended -perfect trades of length , and Steiner trades derived from them. In particular, all Steiner trades with parameters are classified. 相似文献
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