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The codes that they are given are called folded Reed-Solomon codes which are nothing but plain Reed-Solomon codes but viewed as a code over a larger alphabet by careful bundling of codeword symbols. Because of their ubiquity and the nice algebraic properties they possess, list-decoding algorithms for Reed–Solomon codes were a main focus of ...
Reed–Muller codes are linear block codes that are locally testable, locally decodable, and list decodable. These properties make them particularly useful in the design of probabilistically checkable proofs .
The first element of a CIRC decoder is a relatively weak inner (32,28) Reed–Solomon code, shortened from a (255,251) code with 8-bit symbols. This code can correct up to 2 byte errors per 32-byte block.
The default OperandSize and AddressSize to use for each instruction is given by the D bit of the segment descriptor of the current code segment - D=0 makes both 16-bit, D=1 makes both 32-bit. Additionally, they can be overridden on a per-instruction basis with two new instruction prefixes that were introduced in the 80386:
Hence the rate of Hamming codes is R = k / n = 1 − r / (2 r − 1), which is the highest possible for codes with minimum distance of three (i.e., the minimal number of bit changes needed to go from any code word to any other code word is three) and block length 2 r − 1.
FFmpeg (by default decoder only, but see above the compiling options to incorporate the OpenCORE lib) AMR-WB. 3GPP TS 26.173 – AMR-WB speech Codec (C-source code) – reference implementation [11] opencore-amr (decoder), from OpenCORE (one may compile ffmpeg with—enable-libopencore-amrwb to incorporate the OpenCORE lib)
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Syndrome decoding is a highly efficient method of decoding a linear code over a noisy channel, i.e. one on which errors are made. In essence, syndrome decoding is minimum distance decoding using a reduced lookup table. This is allowed by the linearity of the code. [3]