The minimum volume of subspace trades |
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Authors: | Denis S Krotov |
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Institution: | Sobolev Institute of Mathematics, pr. Akademika Koptyuga 4, Novosibirsk 680090, Russia |
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Abstract: | 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. |
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Keywords: | Bitrades Trades Subspace designs |
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