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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.
Creation and annihilation operators. Creation operators and annihilation operators are mathematical operators that have widespread applications in quantum mechanics, notably in the study of quantum harmonic oscillators and many-particle systems. [1] An annihilation operator (usually denoted ) lowers the number of particles in a given state by one.
L (just like p and r) is a vector operator (a vector whose components are operators), i.e. = (,,) where L x, L y, L z are three different quantum-mechanical operators. In the special case of a single particle with no electric charge and no spin , the orbital angular momentum operator can be written in the position basis as:
A generator matrix for a linear [,,]-code has format , where n is the length of a codeword, k is the number of information bits (the dimension of C as a vector subspace), d is the minimum distance of the code, and q is size of the finite field, that is, the number of symbols in the alphabet (thus, q = 2 indicates a binary code, etc.).
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A reactor operator is an individual who has met the licensing requirements of 10 CFR 55 and NUREG-1021 for being a reactor operator. These requirements include: A high school diploma. At least 3 years of power plant experience with at least 1 year of experience at the nuclear power plant where the individual is licensed (not including time ...
Translation operator (quantum mechanics) In quantum mechanics, a translation operator is defined as an operator which shifts particles and fields by a certain amount in a certain direction. It is a special case of the shift operator from functional analysis. More specifically, for any displacement vector , there is a corresponding translation ...
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The term "ladder operator" or "raising and lowering operators" is also sometimes used in mathematics, in the context of the theory of Lie algebras and in particular the affine Lie algebras. For example to describe the su (2) subalgebras, the root system and the highest weight modules can be constructed by means of the ladder operators. [1]
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.