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The QR code, Ver 3 (29×29) uses interleaved blocks. The message has 26 data bytes and is encoded using two Reed-Solomon code blocks. Each block is a (255,233) Reed Solomon code shortened to a (35,13) code. The Delsarte–Goethals–Seidel [12] theorem illustrates an example of an application of shortened Reed–Solomon codes.
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It is used as one of the steps in decoding BCH codes and Reed–Solomon codes ... (PDF), Stanford University, pp. 42– 45, archived from the original (PDF) on June ...
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]
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.
For example: The Reed-Solomon code with LDPC Coded Modulation (RS-LCM) uses a Reed-Solomon outer code. [18] The DVB-S2, the DVB-T2 and the DVB-C2 standards all use a BCH code outer code to mop up residual errors after LDPC decoding. [19] 5G NR uses polar code for the control channels and LDPC for the data channels. [20] [21]
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 ...
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.