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.
Bayreuth , 2016 . - 35 S.

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Abstract

Codes in finite projective spaces with the so-called subspace distance as metric have been proposed for error control in random linear network coding. The resulting 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 $A_2(7,5)=34$.