Reed–Solomon code

A nonbinary error-correcting code formed by evaluating low-degree polynomials over a finite field. Its minimum distance lets it correct symbol errors and recover missing symbols.

Finite field: A finite set with addition, subtraction, multiplication, and division by nonzero elements obeying field axioms. Reed–Solomon symbols and polynomial coefficients are elements of a finite field.
Finite field arithmetic: Addition, subtraction, multiplication, and division performed within a finite field. Field operations define how Reed–Solomon symbols and polynomial values are computed.
Compact Disc digital audio: A digital audio format that stores sampled sound and uses error correction to withstand playback defects. Interleaved Reed–Solomon codes help CDs recover audio despite scratches and contamination.
BCH code: A family of cyclic error-correcting codes with designed distance and algebraic decoding methods. BCH codes can correct bit errors, while Reed–Solomon codes treat field elements as larger symbols.
Polynomial interpolation: The construction of a polynomial from its values at specified points. Decoding reconstructs the transmitted polynomial from sufficiently many correct evaluation points.
Generator polynomial: A polynomial used to define a cyclic code through divisibility constraints on codewords. Cyclic Reed–Solomon implementations use generator polynomials to produce parity symbols.
QR code: A two-dimensional barcode that encodes data in a grid of dark and light modules. QR codes use Reed–Solomon redundancy to recover data when parts of the symbol are damaged.
Binary code: A code whose symbols are bits, with codewords represented as binary strings. Reed–Solomon codes operate on multi-valued field symbols rather than individual bits.
Minimum distance: The smallest number of coordinate positions in which any two distinct codewords differ. For Reed–Solomon codes, the distance determines how many errors or erasures can be corrected.
Code rate: The ratio of information symbols to total encoded symbols in a code. A Reed–Solomon code with parameters n and k carries k information symbols in n symbols.

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