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The Hamming(7,4) code may be written as a cyclic code over GF(2) with generator + +. In fact, any binary Hamming code of the form Ham(r, 2) is equivalent to a cyclic code, [3] and any Hamming code of the form Ham(r,q) with r and q-1 relatively prime is also equivalent to a cyclic code. [4]
Cyclic codes are not only simple to implement but have the benefit of being particularly well suited for the detection of burst errors: contiguous sequences of erroneous data symbols in messages. This is important because burst errors are common transmission errors in many communication channels , including magnetic and optical storage devices.
Circular dependencies can cause many unwanted effects in software programs. Most problematic from a software design point of view is the tight coupling of the mutually dependent modules which reduces or makes impossible the separate re-use of a single module.
This is a list of hash functions, including cyclic redundancy checks, checksum functions, and cryptographic hash functions. This list is incomplete ; you can help by adding missing items . ( February 2024 )
Circular references can appear in computer programming when one piece of code requires the result from another, but that code needs the result from the first. For example, the two functions, posn and plus1 in the following Python program comprise a circular reference: [further explanation needed]
Cyclic codes are a kind of block code with the property that the circular shift of a codeword will always yield another codeword. This motivates the following general definition: For a string s over an alphabet Σ , let shift ( s ) denote the set of circular shifts of s , and for a set L of strings, let shift ( L ) denote the set of all ...
The generator polynomial of the BCH code is defined as the least common multiple g(x) = lcm(m 1 (x),…,m d − 1 (x)). It can be seen that g(x) is a polynomial with coefficients in GF(q) and divides x n − 1. Therefore, the polynomial code defined by g(x) is a cyclic code.
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 .