Let $k$ be a perfect field of characteristic $p>0$. For any positive integers $n$, let $W_n(k)$ be the truncated Witt vectors of length $n$ with coefficients in $k$. For any positive integers $a,b$, is $\textrm{Ext}(W_a(k), W_b(k))$ as an abelian group well understood? Are there any references? Thank you in advance!

Here $\textrm{Ext}(W_a(k), W_b(k))$ is the abelian group that contains all the $W(k)$-modules $M$ (up to isomorphisms) such that $0 \to W_b(k) \to M \to W_a(k) \to 0$ is a short exact sequence of $W(k)$-modules.

over$k$, and not the extensions of $W(k)$-modules (after taking $k$-points)? The former is described in Oort's book, "Commutative Group Schemes", I think, as well as Ch VII of Serre's "Algebraic Groups and Class Fields. The latter seems to depend heavily on the choice of field. – Marty Feb 27 '12 at 19:20