A New Approach to Examine q-Steiner Systems

Tuvi Etzion

Published 2015-07-30Version 1

The interest in $q$-analogs of codes and designs has been increased in the last few years as a consequence of their new application in error-correction for random network coding. Two of the most intriguing problems are the existence question of an infinite family of $q$-analog of Steiner systems, excepts for spreads, and the existence question for $q$-analog for the Fano plane. We exhibit a new method to attack these problems. In the process we define a new family of designs whose existence is implied from the existence of q-analog of Steiner systems, but their existence can be also independent. We present necessary conditions for the existence for such designs, trivial constructions for such designs, and a nontrivial recursive construction.