Construction of large constant dimension codes with a prescribed minimum distance

Titelangaben

Kohnert, Axel ; Kurz, Sascha:
Construction of large constant dimension codes with a prescribed minimum distance.
In: Jacques Calmet, Willi Geiselmann and Jörn Müller-Quade (Hrsg.): Mathematical methods in computer science: essays in memory of Thomas Beth. - Berlin : Springer , 2008 . - S. 31-42 . - (Lecture Notes in Computer Science ; 5393 )
ISBN 978-3-540-89993-8

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Abstract

In this paper we construct constant dimension codes with prescribed minimum distance. There is an increased interest in subspace codes in general since a paper [13] by Kötter and Kschischang where 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 [7] which they used for the construction of designs over finite fields to construct constant dimension
codes. Using this approach we found many new constant dimension codes with a larger number of codewords than previously known codes. We finally give a table of the best constant dimension codes we found.