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A generator matrix is a matrix whose rows form a basis for a linear code. Learn the definition, format, standard form, equivalence, and parity check matrix of a generator matrix in coding theory.
So for a rth order RM code, we have to decode iteratively r+1, times before we arrive at the final received code-word. Also, the values of the message bits are calculated through this scheme; finally we can calculate the codeword by multiplying the message word (just decoded) with the generator matrix.
The Reed–Solomon code is actually a family of codes, where every code is characterised by three parameters: an alphabet size , a block length, and a message length, with <. The set of alphabet symbols is interpreted as the finite field F {\displaystyle F} of order q {\displaystyle q} , and thus, q {\displaystyle q} must be a prime power .
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Hadamard code is a linear error-correcting code based on Hadamard matrices, used for noisy or unreliable channels. Learn about its history, construction, decoding, and examples in coding theory, mathematics, and communication theory.
A parity-check matrix is a matrix that describes the linear relations of a linear block code. It can be used to check and decode codewords, and its minimum distance is the minimum number of linearly independent columns.
Learn how Hamming (7,4) encodes four bits of data into seven bits by adding three parity bits to detect and correct single-bit errors. See the code generator matrix, the parity-check matrix, and the Venn diagram of the overlapping parity coverage.
Codes in general are often denoted by the letter C, and a code of length n and of rank k (i.e., having n code words in its basis and k rows in its generating matrix) is generally referred to as an (n, k) code. Linear block codes are frequently denoted as [n, k, d] codes, where d refers to the code's minimum Hamming distance between any two code ...
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