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- Reed–Solomon_error_correction abstract "In coding theory, Reed–Solomon (RS) codes are non-binary cyclic error-correcting codes invented by Irving S. Reed and Gustave Solomon. They described a systematic way of building codes that could detect and correct multiple random symbol errors. By adding t check symbols to the data, an RS code can detect any combination of up to t erroneous symbols, or correct up to ⌊t/2⌋ symbols. As an erasure code, it can correct up to t known erasures, or it can detect and correct combinations of errors and erasures. Furthermore, RS codes are suitable as multiple-burst bit-error correcting codes, since a sequence of b + 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.In Reed–Solomon coding, source symbols are viewed as coefficients of a polynomial p(x) over a finite field. The original idea was to create n code symbols from k source symbols by oversampling p(x) at n > k distinct points, transmit the sampled points, and use interpolation techniques at the receiver to recover the original message. That is not how RS codes are used today.[citation needed] Instead, RS codes are viewed as cyclic BCH codes, where encoding symbols are derived from the coefficients of a polynomial constructed by multiplying p(x) with a cyclic generator polynomial. This gives rise to efficient decoding algorithms (described below).Reed–Solomon codes have since found important applications from deep-space communication to consumer electronics. They are prominently used in consumer electronics such as CDs, DVDs, Blu-ray Discs, in data transmission technologies such as DSL and WiMAX, in broadcast systems such as DVB and ATSC, and in computer applications such as RAID 6 systems.".
- Reed–Solomon_error_correction wikiPageID "45600".
- Reed–Solomon_error_correction wikiPageRevisionID "599354206".
- Reed–Solomon_error_correction alphabetSize "q = pm".
- Reed–Solomon_error_correction blockLength "n = q − 1".
- Reed–Solomon_error_correction decoding Berlekamp–Massey_algorithm.
- Reed–Solomon_error_correction decoding Euclidean_algorithm.
- Reed–Solomon_error_correction decoding "et al.".
- Reed–Solomon_error_correction distance "n − k + 1".
- Reed–Solomon_error_correction hierarchy BCH_code.
- Reed–Solomon_error_correction hierarchy Block_code.
- Reed–Solomon_error_correction hierarchy Cyclic_code.
- Reed–Solomon_error_correction hierarchy Polynomial_code.
- Reed–Solomon_error_correction hierarchy "Reed–Solomon code".
- Reed–Solomon_error_correction messageLength "k".
- Reed–Solomon_error_correction name "Reed–Solomon codes".
- Reed–Solomon_error_correction namesake "Irving S. Reed and Gustave Solomon".
- Reed–Solomon_error_correction notation "[n, k, n − k + 1]q-code".
- Reed–Solomon_error_correction properties Singleton_bound.
- Reed–Solomon_error_correction subject Category:Coding_theory.
- Reed–Solomon_error_correction subject Category:Error_detection_and_correction.
- Reed–Solomon_error_correction comment "In coding theory, Reed–Solomon (RS) codes are non-binary cyclic error-correcting codes invented by Irving S. Reed and Gustave Solomon. They described a systematic way of building codes that could detect and correct multiple random symbol errors. By adding t check symbols to the data, an RS code can detect any combination of up to t erroneous symbols, or correct up to ⌊t/2⌋ symbols.".
- Reed–Solomon_error_correction label "Code de Reed-Solomon".
- Reed–Solomon_error_correction label "Codice Reed-Solomon".
- Reed–Solomon_error_correction label "Kodowanie korekcyjne Reeda-Solomona".
- Reed–Solomon_error_correction label "Reed-Solomon".
- Reed–Solomon_error_correction label "Reed-Solomon-Code".
- Reed–Solomon_error_correction label "Reed-Solomoncode".
- Reed–Solomon_error_correction label "Reed–Solomon error correction".
- Reed–Solomon_error_correction label "Код Рида — Соломона".
- Reed–Solomon_error_correction label "リード・ソロモン符号".
- Reed–Solomon_error_correction label "里德-所罗门码".
- Reed–Solomon_error_correction sameAs Reed%E2%80%93Solomon_error_correction.
- Reed–Solomon_error_correction sameAs Reedovy-Solomonovy_kódy.
- Reed–Solomon_error_correction sameAs Reed-Solomon-Code.
- Reed–Solomon_error_correction sameAs Reed-Solomon.
- Reed–Solomon_error_correction sameAs Code_de_Reed-Solomon.
- Reed–Solomon_error_correction sameAs Codice_Reed-Solomon.
- Reed–Solomon_error_correction sameAs リード・ソロモン符号.
- Reed–Solomon_error_correction sameAs 리드_솔로몬_부호.
- Reed–Solomon_error_correction sameAs Reed-Solomoncode.
- Reed–Solomon_error_correction sameAs Kodowanie_korekcyjne_Reeda-Solomona.
- Reed–Solomon_error_correction sameAs Q1061598.
- Reed–Solomon_error_correction sameAs Q1061598.
- Reed–Solomon_error_correction wasDerivedFrom Reed–Solomon_error_correction?oldid=599354206.