Binary subspace codes in small ambient spaces

Titelangaben

Heinlein, Daniel ; Kurz, Sascha:
Binary subspace codes in small ambient spaces.
In: Advances in Mathematics of Communications. Bd. 12 (2018) Heft 4 . - S. 817-839.
ISSN 1930-5346
DOI: https://doi.org/10.3934/amc.2018048

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Abstract

Codes in finite projective spaces equipped with the subspace distance have been proposed for error control in random linear network coding. Here we collect the present knowledge on lower and upper bounds for binary subspace codes for projective dimensions of at most $7$. We obtain several improvements of the bounds and perform two classifications of optimal subspace codes, which are unknown so far in the literature.