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Algebraic block codes are typically hard-decoded using algebraic decoders. [jargon] The term block code may also refer to any error-correcting code that acts on a block of bits of input data to produce bits of output data (,). Consequently, the block coder is a memoryless device.
The term algebraic coding theory denotes the sub-field of coding theory where the properties of codes are expressed in algebraic terms and then further researched. [citation needed] Algebraic coding theory is basically divided into two major types of codes: [citation needed] Linear block codes; Convolutional codes
A convolutional code that is terminated is also a 'block code' in that it encodes a block of input data, but the block size of a convolutional code is generally arbitrary, while block codes have a fixed size dictated by their algebraic characteristics. Types of termination for convolutional codes include "tail-biting" and "bit-flushing".
In coding theory, Hamming(7,4) is a linear error-correcting code that encodes four bits of data into seven bits by adding three parity bits. It is a member of a larger family of Hamming codes, but the term Hamming code often refers to this specific code that Richard W. Hamming introduced in 1950.
The codewords in a linear block code are blocks of symbols that are encoded using more symbols than the original value to be sent. [2] A linear code of length n transmits blocks containing n symbols. For example, the [7,4,3] Hamming code is a linear binary code which represents 4-bit messages using 7-bit codewords. Two distinct codewords differ ...
A negacyclic code is a constacyclic code with λ=-1. [8] A quasi-cyclic code has the property that for some s, any cyclic shift of a codeword by s places is again a codeword. [9] A double circulant code is a quasi-cyclic code of even length with s=2. [9] Quasi-twisted codes and multi-twisted codes are further generalizations of constacyclic ...
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The generator polynomial of the BCH code is defined as the least common multiple = ((), …, + ()). Note: if n = q m − 1 {\displaystyle n=q^{m}-1} as in the simplified definition, then g c d ( n , q ) {\displaystyle {\rm {gcd}}(n,q)} is 1, and the order of q {\displaystyle q} modulo n {\displaystyle n} is m . {\displaystyle m.}