Erasure code - Wikipedia
In coding theory, an erasure code is a forward error correction (FEC) code under the assumption of bit erasures (rather than bit errors), which transforms a message of k symbols into a longer message (code word) with n symbols such that the original message can be recovered from a subset of the n symbols. The fraction r = k/n is called the code rate. The fraction k’/k, where k’ denotes the number of symbols required for recovery, is called reception efficiency. The recovery algorithm expects that it is known which of the n symbols are lost — unlike forward error correction codes.
Optimal erasure codes have the property that any k out of the n code word symbols are sufficient to recover the original message (i.e., they have optimal reception efficiency). Optimal erasure codes are maximum distance separable codes (MDS codes).
Parity check is the special case where n = k + 1. From a set of k values { v i } 1 ≤ i ≤ k {\displaystyle \{v_{i}\}_{1\leq i\leq k}} , a checksum is computed and appended to the k source values:
