= Erasure
{disambiguate=coding theory}
An erasure is a missing or explicitly flagged symbol of a transmitted <codeword>; its position is known to the decoder. An error instead replaces a symbol by an incorrect value without revealing its location. This distinction changes how much redundancy is needed.
A <block code> of <minimum distance> $d$ uniquely corrects every <erasure (coding theory)> pattern of size at most $d-1$. Indeed, two different <codewords> agreeing at all unerased positions could differ in at most the erased positions, contradicting their distance of at least $d$. Conversely, erasing all differing positions of a minimum-distance pair makes that pair indistinguishable.
For the binary even-parity code $\{000,011,101,110\}$, one erased <bit> is recovered from the other two: the missing value is their sum modulo two. One arbitrary unflagged error is only detectable, because the <minimum distance> is two. More generally, $e$ errors and $s$ erasures are uniquely correctable whenever $2e+s<d$.
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