---
author:
- |
    [Lu Lu,   Qiongxiang Huang[^1],   Jiangxia Hou[^2]]{}\
    College of Mathematics and Systems Science, Xinjiang University, Urumqi, Xinjiang 830046, P.R.China
title: 'Infinite classes of strongly regular graphs derived from $GL(n,F_2)$[^3]'
---

It is known that the automorphism group of the elementary abelian $2$-group $Z_2^n$ is isomorphic to the general linear group $GL(n,F_2)$ of degree $n$ over $F_2$. Let $W$ be the collection of permutation matrices of order $n$. It is clear that $W\le GL(n,F_2)$. In virtue of this, we consider the Cayley graph $Cay(Z_2^n,S)$, where $S$ is the union of some orbits under the action of $W$. We call such graphs the orbit Cayley graphs over $Z_2^n$. In this paper, we give eight infinite families of strongly regular graphs among orbit Cayley graphs over $Z_2^n$, in which six families are new as we know. By the way, we formulate the spectra of orbit Cayley graphs as well.

**Keywords:** Cayley graph; Strongly regular graph; Vector space; Galois field

**AMS subject classifications:** 05A19; 05C50; 05C25

Introduction
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Let $\Gamma$ be a graph with vertex set $V=\{v_1,\ldots,v_n\}$. The *adjacency matrix* of $\Gamma$, denoted by $A(\Gamma)=(a_{i,j})_{n\times n}$, is the $n\times n$ matrix such that the $a_{i,j}=1$ if $v_i\sim v_j$ and $0$ otherwise. 