  A code $C$ is a subset of the vertex set of a graph and $C$ is
$s$-neighbour-transitive if its automorphism group ${\rm Aut}(C)$ acts
transitively on each of the first $s+1$ parts $C_0,C_1,\ldots,C_s$ of the
distance partition $\{C=C_0,C_1,\ldots,C_\rho\}$, where $\rho$ is the covering
radius of $C$. While codes have traditionally been studied in the Hamming and
Johnson graphs, we consider here codes in the Kneser graphs. Let $\Omega$ be
the underlying set on which the Kneser graph $K(n,k)$ is defined. Our first
main result says that if $C$ is a $2$-neighbour-transitive code in $K(n,k)$
such that $C$ has minimum distance at least $5$, then $n=2k+1$ (i.e., $C$ is a
code in an odd graph) and $C$ lies in a particular infinite family or is one
particular sporadic example. We then prove several results when $C$ is a
neighbour-transitive code in the Kneser graph $K(n,k)$. First, if ${\rm
Aut}(C)$ acts intransitively on $\Omega$ we characterise $C$ in terms of
certain parameters. We then assume that ${\rm Aut}(C)$ acts transitively on
$\Omega$, first proving that if $C$ has minimum distance at least $3$ then
either $K(n,k)$ is an odd graph or ${\rm Aut}(C)$ has a $2$-homogeneous (and
hence primitive) action on $\Omega$. We then assume that $C$ is a code in an
odd graph and ${\rm Aut}(C)$ acts imprimitively on $\Omega$ and characterise
$C$ in terms of certain parameters. We give examples in each of these cases and
pose several open problems.
