Erasure (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 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 $2e+s<d$.