Editing Reed–Solomon error correction (section)

===Data transmission===
Specialized forms of Reed–Solomon codes, specifically [[Cauchy matrix|Cauchy]]-RS and [[Vandermonde matrix|Vandermonde]]-RS, can be used to overcome the unreliable nature of data transmission over [[Binary erasure channel|erasure channels]]. The encoding process assumes a code of RS(''N'',&nbsp;''K'') which results in ''N'' codewords of length ''N'' symbols each storing ''K'' symbols of data, being generated, that are then sent over an erasure channel.

Any combination of ''K'' codewords received at the other end is enough to reconstruct all of the ''N'' codewords. The code rate is generally set to 1/2 unless the channel's erasure likelihood can be adequately modelled and is seen to be less. In conclusion, ''N'' is usually 2''K'', meaning that at least half of all the codewords sent must be received in order to reconstruct all of the codewords sent.

Reed–Solomon codes are also used in [[xDSL]] systems and [[CCSDS]]'s [[Space Communications Protocol Specifications]] as a form of [[forward error correction]].