EC = error correction?

erasure = we know the place of failure (erroneous stripe)

error (silent data corruption) = we do NOT know the place of failure

$ P $ and $ Q $ --- syndromes?


If $ D_0,\dots,D_{k-1} $ --- information strips, then
$$ P=D_0+D_1+\dots+D_{k-1}, \quad ( + = XOR ) $$
$$ Q=D_0\mathfrak A^{k-1}+ D_1\mathfrak A^{k-2}+\dots+D_{k-1}  $$
where $ \mathfrak A $ stands for a primitive element of the finite field.

Is this true?