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For each integer r ≥ 2 there is a code-word with block length n = 2 r − 1 and message length k = 2 r − r − 1. 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 ...
For a fixed length n, the Hamming distance is a metric on the set of the words of length n (also known as a Hamming space), as it fulfills the conditions of non-negativity, symmetry, the Hamming distance of two words is 0 if and only if the two words are identical, and it satisfies the triangle inequality as well: [2] Indeed, if we fix three words a, b and c, then whenever there is a ...
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 ...
In coding theory, the Singleton bound, named after Richard Collom Singleton, is a relatively crude upper bound on the size of an arbitrary block code with block length , size and minimum distance . It is also known as the Joshibound [ 1 ] proved by Joshi (1958) and even earlier by Komamiya (1953) .
Consequently, double-block-length compression functions output twice the number of bits. If a block cipher has a block size of say 128 bits single-block-length methods create a hash function that has the block size of 128 bits and produces a hash of 128 bits. Double-block-length methods make hashes with double the hash size compared to the ...
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In typography, line length is the width of a block of typeset text, usually measured in units of length like inches or points or in characters per line (in which case it is a measure). A block of text or paragraph has a maximum line length that fits a determined design. If the lines are too short then the text becomes disjointed; if they are ...
An (,) quasi-cyclic code is a linear block code such that, for some which is coprime to , the polynomial () is a codeword polynomial whenever () is a codeword polynomial. Here, codeword polynomial is an element of a linear code whose code words are polynomials that are divisible by a polynomial of shorter length called the generator polynomial .