Bounds on the cardinality of subspace codes with non-maximum code distance

EM Gabidulin, NI Pilipchuk, OV Trushina - Problems of Information …, 2021 - Springer
EM Gabidulin, NI Pilipchuk, OV Trushina
Problems of Information Transmission, 2021Springer
We study subspace codes with nonmaximum code distance. As opposed to spreads, ie,
codes with the maximum subspace distance, we refer to them as nonspreads here. We
consider families of nonspreads based on using the Silva–Kötter–Kschischang (SKK)
subspace code construction and Gabidulin–Bossert multicomponent codes with zero prefix
(MZP). We give estimates for cardinalities of nonspreads for a large number of parameters.
We show that for large dimensions, the cardinalities almost attain the upper bound given by …
Abstract
We study subspace codes with nonmaximum code distance. As opposed to spreads, i.e., codes with the maximum subspace distance, we refer to them as nonspreads here. We consider families of nonspreads based on using the Silva–Kötter–Kschischang (SKK) subspace code construction and Gabidulin–Bossert multicomponent codes with zero prefix (MZP). We give estimates for cardinalities of nonspreads for a large number of parameters. We show that for large dimensions, the cardinalities almost attain the upper bound given by the Johnson inequality.
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