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arXiv · 1512.06660

Constructions and Bounds for Mixed-Dimension Subspace Codes

Thomas Honold·Michael Kiermaier·Sascha Kurz
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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 \emph{Main Problem of Subspace Coding} is to determine the maximum size $A_q(v,d)$ of a code in $\operatorname{PG}(v-1,\mathbb{F}_q)$ with minimum subspace distance $d$. Here we completely resolve this problem for $d\ge v-1$. 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 $A_2(v,d)$, $v\leq 7$.

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Thomas Honold, Michael Kiermaier, Sascha Kurz. 2018-08-29. Constructions and Bounds for Mixed-Dimension Subspace Codes. https://arxiv.org/abs/1512.06660

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