View source for Reed-Solomon codes

'''Reed-Solomon codes''' are a class of non-binary cyclic [[Error-Correcting Codes|error-correcting codes]] invented by Irving Reed and Gustave Solomon in 1960. They operate by treating a message as the coefficients of a polynomial over a [[Finite Field|finite field]] and transmitting the polynomial's values at selected points; decoding recovers the polynomial even when some values are corrupted, using the algebraic fact that a degree-''k'' polynomial is uniquely determined by any ''k+1'' correct evaluations.

Reed-Solomon codes are the workhorse of deep-space and optical communication: the [[Voyager Spacecraft|Voyager probes]], [[CD-ROM|compact discs]], [[QR Codes|QR codes]], and [[RAID|RAID storage systems]] all depend on them. Their error-correcting power comes from the algebraic structure of [[Finite Field|finite fields]], not from probabilistic iteration — making them a fundamentally different architectural family from [[Turbo Codes|turbo codes]] or [[LDPC Codes|LDPC codes]]. The [[BCH Codes|BCH codes]], which generalize Reed-Solomon to binary alphabets, share this algebraic lineage and represent a rival tradition in coding theory: one that trusts mathematical structure over iterative approximation.

[[Category:Technology]][[Category:Mathematics]]