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In 1973, Tietäväinen proved [1] that any non-trivial perfect code over a prime-power alphabet has the parameters of a Hamming code or a Golay code. A perfect code may be interpreted as one in which the balls of Hamming radius t centered on codewords exactly fill out the space ( t is the covering radius = packing radius).
Under this definition codes such as turbo codes, terminated convolutional codes and other iteratively decodable codes (turbo-like codes) would also be considered block codes. A non-terminated convolutional encoder would be an example of a non-block (unframed) code, which has memory and is instead classified as a tree code .
According to software engineer Robert Wills, Buzz Aldrin entered the codes to request that the computer display altitude and other data on the computer’s screen. The system was designed to support seven simultaneous programs running, but Aldrin’s request was the eighth.
In a polynomial code over () with code length and generator polynomial () of degree , there will be exactly code words. Indeed, by definition, () is a code word if and only if it is of the form () = (), where () (the quotient) is of degree less than .
Hamming graphs are a special class of graphs named after Richard Hamming and used in several branches of mathematics (graph theory) and computer science. Let S be a set of q elements and d a positive integer. The Hamming graph H(d,q) has vertex set S d, the set of ordered d-tuples of elements of S, or sequences of length d from S.
This code has minimal Hamming distance 15 and corrects 7 errors. It has 1 data bit and 14 checksum bits. ... Definition. Fix a finite field (), ...
One 64 GiB DDR5-4800 ECC 1.1 V RDIMM. Registered, or buffered, memory is not the same as ECC; the technologies perform different functions. It is usual for memory used in servers to be both registered, to allow many memory modules to be used without electrical problems, and ECC, for data integrity.
A code is defined to be equidistant if and only if there exists some constant d such that the distance between any two of the code's distinct codewords is equal to d. [4] In 1984 Arrigo Bonisoli determined the structure of linear one-weight codes over finite fields and proved that every equidistant linear code is a sequence of dual Hamming ...