  Let $p\neq3$ be any prime and $l\neq3$ be any odd prime with $gcd(p,l)=1$.
$F_{q}^{*}=\langle\xi\rangle$ is decomposed into mutually disjoint union of
$gcd(q-1,3lp^{s})$ coset over the subgroup $\langle\xi^{3lp^{s}}\rangle$, where
$\xi$ is a primitive $(q-1)$th root of unity. We classify all repeated-root
constacyclic codes of length $3lp^{s}$ over the finite field $F_{q}$ into some
equivalence classes by the decomposition, where $q=p^{m}$, $s$ and $m$ are
positive integers. According to the equivalence classes, we explicitly
determine the generator polynomials of all repeated-root constacyclic codes of
length $3lp^{s}$ over $F_{q}$ and their dual codes. Self-dual
cyclic(negacyclic) codes of length $3lp^{s}$ over $F_{q}$ exist only when
$p=2$. And we give all self-dual cyclic(negacyclic) codes of length
$3l2^{s}$over $F_{2^{m}}$ and its enumeration.
