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Erasure code
In information theory, an erasure code is a forward error correction (FEC) code for the binary erasure channel, 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.
==Optimal erasure 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).
Optimal codes are often costly (in terms of memory usage, CPU time, or both) when ''n'' is large. Except for very simple schemes, practical solutions usually have quadratic encoding and decoding complexity. In 2014, Lin et al. 〔Sian-Jheng Lin, Wei-Ho Chung, and Yunghsiang S. Han, "Novel polynomial basis and its application to Reed-Solomon erasure codes", The 55th Annual Symposium on Foundations of Computer Science (FOCS 2014). 〕 gave an approach with operations.
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