Construction of Large Constant Dimension Codes With a Prescribed Minimum Distance

TL;DR

This paper presents a novel method for constructing large constant dimension space codes with a prescribed minimum distance, improving the number of codewords over previous codes and relevant for network coding and finite field design theory.

Contribution

It adapts a design construction method over finite fields to create larger constant dimension codes with specific minimum distances.

Findings

Many new constant dimension space codes discovered

Codes have larger size than previously known

A table of best codes is provided

Abstract

In this paper we construct constant dimension space codes with prescribed minimum distance. There is an increased interest in space codes since a paper by Koetter and Kschischang were they gave an application in network coding. There is also a connection to the theory of designs over finite fields. We will modify a method of Braun, Kerber and Laue which they used for the construction of designs over finite fields to do the construction of space codes. Using this approach we found many new constant dimension spaces codes with a larger number of codewords than previously known codes. We will finally give a table of the best found constant dimension space codes.