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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.
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]
The most popular erasure codes are Reed-Solomon coding, Low-density parity-check code (LDPC codes), and Turbo codes. [ 1 ] As of 2023, modern data storage systems can be designed to tolerate the complete failure of a few disks without data loss, using one of 3 approaches: [ 2 ] [ 3 ] [ 4 ]
The term "folded Reed–Solomon codes" was coined in a paper by V.Y. Krachkovsky with an algorithm that presented Reed–Solomon codes with many random "phased burst" errors. [1] The list-decoding algorithm for folded RS codes corrects beyond the 1 − R {\displaystyle 1-{\sqrt {R}}} bound for Reed–Solomon codes achieved by the Guruswami ...
This page was last edited on 2 September 2006, at 06:55 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.
This page was last edited on 26 January 2025, at 03:50 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.
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.