Coset Construction for Subspace Codes

Titelangaben

Heinlein, Daniel ; Kurz, Sascha:
Coset Construction for Subspace Codes.
2016
Veranstaltung: Network Coding and Designs , 4.-8.04.2016 , Dubrovnik, Kroatien.
(Veranstaltungsbeitrag: Kongress/Konferenz/Symposium/Tagung , Vortrag )

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Abstract

One of the main problems of the research area of network coding is to compute good lower and upper bounds of the achievable so-called subspace codes in PG$(n,q)$ for a given minimal distance. Here we generalize a construction of Etzion and Silberstein to a wide range of parameters. This construction, named coset construction, improves several of the previously best known subspace codes and attains the MRD bound for an infinite family of parameters:

Theorem:
For each $k\ge 4$ and arbitrary $q$ we have
$$
A_q(3k-3,2k-2;k)\ge q^{4k-6}+\frac{q^{2k-3}-q}{q^{k-2}-1}-q+1.
$$

and

Theorem:
$A_2(10,6;4)\ge 4173$.