On the cardinality of matrices with prescribed rank and partial trace over a finite field

Kumar Balasubramanian, Krishna Kaipa, Himanshi Khurana

Let $F$ be the finite field of order $q$ and $\M(n,r, F)$ be the set of $n\times n$ matrices of rank $r$ over the field $F$. For $\alpha \in F$ and $A\in \M(n,F)$, let $$Z^α_{A,r}=\left\…