Constructions and Bounds for MixedDimension Subspace Codes
Abstract
Codes in finite projective spaces equipped with the subspace distance have been proposed for error control in random linear network coding. The resulting socalled \emph{Main Problem of Subspace Coding} is to determine the maximum size $A_q(v,d)$ of a code in $\operatorname{PG}(v1,\mathbb{F}_q)$ with minimum subspace distance $d$. Here we completely resolve this problem for $d\ge v1$. For $d=v2$ 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 $A_2(v,d)$, $v\leq 7$.
 Publication:

arXiv eprints
 Pub Date:
 December 2015
 arXiv:
 arXiv:1512.06660
 Bibcode:
 2015arXiv151206660H
 Keywords:

 Mathematics  Combinatorics;
 Computer Science  Information Theory;
 94B05;
 05B25;
 51E20 (Primary);
 51E14;
 51E22;
 51E23 (Secondary)
 EPrint:
 35 pages, 2 tables, typo corrected