  I define higher codimensional versions of contact structures on manifolds as
maximally non-integrable distributions. I call them multicontact structures.
Cartan distributions on jet spaces provide canonical examples. More generally,
I define higher codimensional versions of pre-contact structures as
distributions on manifolds whose characteristic symmetries span a constant
dimensional distribution. I call them pre-multicontact structures. Every
distribution is almost everywhere, locally, a pre-multicontact structure. After
showing that the standard symplectization of contact manifolds generalizes
naturally to a (pre-)multisymplectization of (pre-)multicontact manifolds, I
make use of results by C. Rogers and M. Zambon to associate a canonical
$L_{\infty}$-algebra to any (pre-)multicontact structure. Such
$L_{\infty}$-algebra is a multicontact version of the Jacobi bracket on a
contact manifold. However, unlike the multisymplectic $L_\infty$-algebra of
Rogers and Zambon, the multicontact $L_\infty$-algebra is always a homological
resolution of a Lie algebra. Finally, I describe in local coordinates the
$L_{\infty}$-algebra associated to the Cartan distribution on jet spaces.
