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The Reed–Solomon code is a [n, k, n − k + 1] code; in other words, it is a linear block code of length n (over F) with dimension k and minimum Hamming distance = + The Reed–Solomon code is optimal in the sense that the minimum distance has the maximum value possible for a linear code of size ( n , k ); this is known as the Singleton bound .
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Reed-Solomon codes are used in compact discs to correct errors caused by scratches. Modern hard drives use Reed–Solomon codes to detect and correct minor errors in sector reads, and to recover corrupted data from failing sectors and store that data in the spare sectors. [20]
Erasure coding was invented by Irving Reed and Gustave Solomon in 1960. [1]There are many different erasure coding schemes. The most popular erasure codes are Reed-Solomon coding, Low-density parity-check code (LDPC codes), and Turbo codes.
Algebraic geometry codes are a generalization of Reed–Solomon codes. Constructed by Irving Reed and Gustave Solomon in 1960, Reed–Solomon codes use univariate polynomials to form codewords, by evaluating polynomials of sufficiently small degree at the points in a finite field. [8] Formally, Reed–Solomon codes are defined in the following way.
The combination of an inner Viterbi convolutional code with an outer Reed–Solomon code (known as an RSV code) was first used in Voyager 2, [5] [8] and it became a popular construction both within and outside of the space sector.
This is a decoder algorithm that efficiently corrects errors in Reed–Solomon codes for an RS(n, k), code based on the Reed Solomon original view where a message ,, is used as coefficients of a polynomial () or used with Lagrange interpolation to generate the polynomial () of degree < k for inputs ,, and then () is applied to +,, to create an ...
Justesen codes are derived as the code concatenation of a Reed–Solomon code and the Wozencraft ensemble. The Reed–Solomon codes used achieve constant rate and constant relative distance at the expense of an alphabet size that is linear in the message length.