  Let $A_q(n,d)$ be the maximum order (maximum number of codewords) of a
$q$-ary code of length $n$ and Hamming distance at least $d$. And let
$A(n,d,w)$ that of a binary code of constant weight $w$. Building on results
from algebraic graph theory and Erd\H{o}s-ko-Rado like theorems in extremal
combinatorics, we show how several known bounds on $A_q(n,d)$ and $A(n,d,w)$
can be easily obtained in a single framework. For instance, both the Hamming
and Singleton bounds can derived as an application of a property relating the
clique number and the independence number of vertex transitive graphs. Using
the same techniques, we also derive some new bounds and present some additional
applications.
