Frames as continuous redundant codes

We consider expansions in a finite frame as a continuous linear redundant coding and show that coding of an element from an $N$-dimensional space with a frame consisting of $(N+M)$ elements provides detection of up to $M$ errors and correction of up to $\left\lfloor\frac{M}{2}\right\rfloor$ errors. We also note that these results are sharp. The presented results are direct continuous analogues of classical statements from the discrete coding theory.