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The modern binary number system, the basis for binary code, is an invention by Gottfried Leibniz in 1689 and appears in his article Explication de l'Arithmétique Binaire (English: Explanation of the Binary Arithmetic) which uses only the characters 1 and 0, and some remarks on its usefulness. Leibniz's system uses 0 and 1, like the modern ...
In computing, code generation denotes software techniques or systems that generate program code which may then be used independently of the generator system in a runtime environment. Specific articles: Code generation (compiler), a mechanism to produce the executable form of computer programs, such as machine code, in some automatic manner
For the purposes of Hamming codes, two Hamming matrices can be defined: the code generator matrix G and the parity-check matrix H: := ... 00 0 1 111 0: 1111: 11 1 1 111:
The Hadamard code is a linear code, and all linear codes can be generated by a generator matrix. This is a matrix such that Had ( x ) = x ⋅ G {\displaystyle {\text{Had}}(x)=x\cdot G} holds for all x ∈ { 0 , 1 } k {\displaystyle x\in \{0,1\}^{k}} , where the message x {\displaystyle x} is viewed as a row vector and the vector-matrix product ...
Another use for the Miracle Octad Generator is to quickly verify codewords of the binary Golay code.Each element of the Miracle Octad Generator can store either a '1' or a '0', usually displayed as an asterisk and blank space, respectively.
Wichmann–Hill is a pseudorandom number generator proposed in 1982 by Brian Wichmann and David Hill. [1] It consists of three linear congruential generators with different prime moduli, each of which is used to produce a uniformly distributed number between 0 and 1. These are summed, modulo 1, to produce the result. [2]
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