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Reference.org
Reed–Solomon error correction
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<p>In <a href="/facts/Information_theory/qNLH3U5P">information theory</a> and <a href="/facts/Coding_theory/SBqStoGL">coding theory</a>, Reed–Solomon codes are a group of <a href="/facts/Error-correcting_code/cLUTUJrA">error-correcting codes</a> that were introduced by <a href="/facts/Irving_S._Reed/tuxmsa6G">Irving S. Reed</a> and <a href="/facts/Gustave_Solomon/2APnUPsu">Gustave Solomon</a> in 1960. They have many applications, including consumer technologies such as <a href="/facts/MiniDisc/yF3LYCqL">MiniDiscs</a>, <a href="/facts/CD/0IntaWNj">CDs</a>, <a href="/facts/DVD/7fJsHJrN">DVDs</a>, <a href="/facts/Blu-ray/zyPalhfG">Blu-ray</a> discs, <a href="/facts/QR_code/B0l0IS7a">QR codes</a>, <a href="/facts/Data_Matrix/CDENxAJS">Data Matrix</a>, <a href="/facts/Data_transmission/1yAhaANd">data transmission</a> technologies such as <a href="/facts/DSL/3pY5osov">DSL</a> and <a href="/facts/WiMAX/tz9zpKHU">WiMAX</a>, <a href="/facts/Broadcasting/AV1f3dGy">broadcast</a> systems such as satellite communications, <a href="/facts/Digital_Video_Broadcasting/KPGNTGBJ">DVB</a> and <a href="/facts/ATSC_Standards/RIYWmB7v">ATSC</a>, and storage systems such as <a href="/facts/RAID_6/StvCqldY">RAID 6</a>. </p><p>Reed–Solomon codes operate on a block of data treated as a set of <a href="/facts/Finite_field/UkMGJo3m">finite-field</a> elements called symbols. Reed–Solomon codes are able to detect and correct multiple symbol errors. By adding <i>t</i> = <i>n</i> − <i>k</i> check symbols to the data, a Reed–Solomon code can detect (but not correct) any combination of up to t erroneous symbols, <i>or</i> locate and correct up to ⌊<i>t</i>/2⌋ erroneous symbols at unknown locations. As an <a href="/facts/Erasure_code/ea1C1z2X">erasure code</a>, it can correct up to t erasures at locations that are known and provided to the algorithm, or it can detect and correct combinations of errors and erasures. Reed–Solomon codes are also suitable as multiple-<a href="/facts/Burst_error/UXkhCd2D">burst</a> bit-error correcting codes, since a sequence of <i>b</i> + 1 consecutive bit errors can affect at most two symbols of size b. The choice of t is up to the designer of the code and may be selected within wide limits. </p><p>There are two basic types of Reed–Solomon codes – original view and <a href="/facts/BCH_code/1KelJGxF">BCH</a> view – with BCH view being the most common, as BCH view decoders are faster and require less working storage than original view decoders. </p>