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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 ...
Reed–Muller codes are linear block codes that are locally testable, locally decodable, and list decodable. These properties make them particularly useful in the design of probabilistically checkable proofs . Traditional Reed–Muller codes are binary codes, which means that messages and codewords are binary strings.
The binary Golay code, G 23 is a perfect code. That is, the spheres of radius three around code words form a partition of the vector space. G 23 is a 12-dimensional subspace of the space F 23 2. The automorphism group of the perfect binary Golay code G 23 (meaning the subgroup of the group S 23 of permutations of the coordinates of F 23
Convolutional code with any code rate can be designed based on polynomial selection; however, in practice, a puncturing procedure is often used to achieve the required code rate. Puncturing is a technique used to make a m/n rate code from a "basic" low-rate (e.g., 1/n) code. It is achieved by deleting of some bits in the encoder output.
Pseudorandom noise. In cryptography, pseudorandom noise ( PRN [1]) is a signal similar to noise which satisfies one or more of the standard tests for statistical randomness. Although it seems to lack any definite pattern, pseudorandom noise consists of a deterministic sequence of pulses that will repeat itself after its period.
Code generation (compiler) In computing, code generation is part of the process chain of a compiler and converts intermediate representation of source code into a form (e.g., machine code) that can be readily executed by the target system. Sophisticated compilers typically perform multiple passes over various intermediate forms.
A linear code of length n and dimension k is a linear subspace C with dimension k of the vector space where is the finite field with q elements. Such a code is called a q -ary code. If q = 2 or q = 3, the code is described as a binary code, or a ternary code respectively. The vectors in C are called codewords.
Event generator. Event generators are software libraries that generate simulated high-energy particle physics events. [1] [2] They randomly generate events as those produced in particle accelerators, collider experiments or the early universe. Events come in different types called processes as discussed in the Automatic calculation of particle ...