A symplectic fission scheme for the association scheme of rectangular matrices and its automorphisms

Abstract

In this paper, a symplectic fission scheme for the association scheme of $ m\times n $ rectangular matrices over the finite field $ \mathbb{F}_q $, denoted by $ {\rm{SMat}}(m\times n, q) $, is constructed, where $ q $ is a power of a prime number. We discuss its association classes and inner automorphism group. In particular, we determine the intersection numbers and automorphism group of $ {\rm{SMat}}(m\times n, q) $ for $ m = 1 $ and $ m = 2 $.

Keywords

• association scheme
• fission scheme
• intersection number
• automorphism