$q$-Analogs of Covering Designs and Steiner Systems Based on Singular Linear Space

Abstract

In this paper, $q$-analogs of covering designs and Steiner systems based on the subspaces of type $(m,0)$ and the subspaces of type $(m_1,0)$ in singular linear space ${\mathbb{F}}_q^{(n+l)}$ over ${\mathbb{F}}_q$ are presented, where $m_1<m$. Then the properties about $q$-analogs of covering designs and Steiner systems are discussed.