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Combining subspace codes

The work of the first, third and fourth author was supported by the Italian National Group for Algebraic and Geometric Structures and their Applications (GNSAGA–INdAM)

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  • In the context of constant-dimension subspace codes, an important problem is to determine the largest possible size $ A_q(n, d; k) $ of codes whose codewords are $ k $-subspaces of $ {\mathbb F}_q^n $ with minimum subspace distance $ d $. Here in order to obtain improved constructions, we investigate several approaches to combine subspace codes. This allow us to present improvements on the lower bounds for constant-dimension subspace codes for many parameters, including $ A_q(10, 4; 5) $, $ A_q(12, 4; 4) $, $ A_q(12, 6, 6) $ and $ A_q(16, 4; 4) $.

    Mathematics Subject Classification: Primary: 51E20; Secondary: 05B25, 94B65.


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