Let \(X,Y\subset \{0,1\}^*\). We say Y codes X if every \(x\in X\) can be obtained by applying a short program to some \(y\in Y\). We are interested in sets Y that code X robustly in the sense that even if we delete an arbitrary subset Y'\(\subset Y\) of size k, say, the remaining set of strings \(Y\setminus Y'\) still codes X. In general, this can be achieved only by making in some sense more than k copies of each \(x\in X\) and distributing these copies on different strings Y. Thus if the strings in X and Y have the same length, then {\#}Y\(\geq (k+1)\#X\). If we allow coding of X by Y in a way that every \(x\in X\) is obtained from strings x,z\(\in Y\) by application of a short program, then we can do better. Let \(Y=\{\oplus_{x\in S}x|\) \(S\subset X\}\) where \(\oplus\) denotes bitwise sum mod 2. Then {\#}Y\(=2^{*x}\). Yet Y codes X robustly for \(k=2^{*x-1}-1\). This paper explores the limitations of coding schemes of this nature.