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Bounds on the Cardinality of Subspace Codes with Non-maximum Code Distance

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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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Authors and Affiliations

  1. Moscow Institute of Physics and Technology (State University), Moscow, Russia

    N. I. Pilipchuk & O. V. Trushina

Authors
  1. E. M. Gabidulin
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  2. N. I. Pilipchuk
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  3. O. V. Trushina
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Additional information

Translated from Problemy Peredachi Informatsii, 2021, Vol. 57, No. 3, pp. 48–54 https://doi.org/10.31857/S0555292321030037.

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Gabidulin, E., Pilipchuk, N. & Trushina, O. Bounds on the Cardinality of Subspace Codes with Non-maximum Code Distance. Probl Inf Transm 57, 241–247 (2021). https://doi.org/10.1134/S0032946021030030

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  • DOI: https://doi.org/10.1134/S0032946021030030

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