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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.
Morse code is a method used in telecommunication to encode text characters as standardized sequences of two different signal durations, called dots and dashes, or dits and dahs. [3] [4] Morse code is named after Samuel Morse, one of the early developers of the system adopted for electrical telegraphy .
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.
A magnetohydrodynamic generator ( MHD generator) is a magnetohydrodynamic converter that transforms thermal energy and kinetic energy directly into electricity. An MHD generator, like a conventional generator, relies on moving a conductor through a magnetic field to generate electric current. The MHD generator uses hot conductive ionized gas (a ...
Its generator polynomial as a cyclic code is given by. where is the set of quadratic residues of in the set and is a primitive th root of unity in some finite extension field of . The condition that is a quadratic residue of ensures that the coefficients of lie in . The dimension of the code is . Replacing by another primitive -th root of unity ...
Mathematical definition. In mathematical terms, the extended binary Golay code G24 consists of a 12-dimensional linear subspace W of the space V = F24. 2 of 24-bit words such that any two distinct elements of W differ in at least 8 coordinates. W is called a linear code because it is a vector space. In all, W comprises 4096 = 212 elements.