Binary Subspace Codes in Small Ambient Spaces
Daniel Heinlein, Sascha Kurz
TL;DR
This paper reviews and improves bounds for binary subspace codes in small projective spaces, providing new classifications of optimal codes for dimensions up to 7, advancing error control in network coding.
Contribution
It offers improved bounds and the first classifications of optimal binary subspace codes in small ambient spaces, filling gaps in existing knowledge.
Findings
Improved bounds for binary subspace codes up to dimension 7
Two classifications of optimal subspace codes
Enhanced understanding of code structures in small spaces
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 . We obtain several improvements of the bounds and perform two classifications of optimal subspace codes, which are unknown so far in the literature.
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