Constructions and bounds for mixed-dimension subspace codes

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Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
Constructions and bounds for mixed-dimension subspace codes.
In: Advances in Mathematics of Communications. Bd. 10 (2016) Heft 3 . - S. 649-682.
ISSN 1930-5346
DOI: https://doi.org/10.3934/amc.2016033

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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. The resulting so-called Main Problem of Subspace Coding is to determine the maximum size A_q(v,d) of a code in PG(v−1,F_q) with minimum subspace distance d. Here we completely resolve this problem for d>=v−1. For d=v−2 we present some improved bounds and determine A_q(5,3)=2q^3+2 (all q), A_2(7,5)=34. We also provide an exposition of the known determination of A_q(v,2), and a table with exact results and bounds for the numbers A_2(v,d), v<=7.