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• W2925030464 abstract "A characteristic-dependent linear rank inequality is a linear inequality that holds by ranks of subspaces of a vector space over a finite field of determined characteristic, and does not in general hold over other characteristics. In this paper, we produce new characteristic-dependent linear rank inequalities by an alternative technique to the usual Dougherty's inverse function method [9]. We take up some ideas of Blasiak [4], applied to certain complementary vector spaces, in order to produce them. Also, we present some applications to network coding. In particular, for each finite or co-finite set of primes $P$, we show that there exists a sequence of networks $mathcal{N}left(kright)$ in which each member is linearly solvable over a field if and only if the characteristic of the field is in $P$, and the linear capacity, over fields whose characteristic is not in $P$, $rightarrow0$ as $krightarrowinfty$." @default.
• W2925030464 created "2019-04-01" @default.
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• W2925030464 date "2019-03-27" @default.
• W2925030464 modified "2023-09-25" @default.
• W2925030464 title "Characteristic-Dependent Linear Rank Inequalities via Complementary Vector Spaces" @default.
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