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Optimal erasure codes produce ''n/r'' blocks where any ''n'' blocks is sufficient to recover the original message.
Optimal codes are often costly (in terms of memory usage, CPU time or both) when n is large.
===Parity Check===
Parity check is the simplest erasure codes. From a set of k values <math>\{v_i\}_{1\leq i \leq k}</math>, a check-sum is computed and appended to the k source values:<br />
<math>v_{k+1}= - \sum_{i=1}^{k}v_i</math>. <br />
The set of k+1 values <math>\{v_i\}_{1\leq i \leq k+1}</math> is now consistent with regard to the check-sum.
If one of this values <math>v_e</math> is erased, it can be easily recovered by summing the remaining variables: <br />
<math>v_{e}= - \sum_{i=1 ,i \neq e }^{k+1}v_i</math>.
===Err-mail===
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