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In linear algebra terms, the dual code is the annihilator of C with respect to the bilinear form . The dimension of C and its dual always add up to the length n : A generator matrix for the dual code is the parity-check matrix for the original code and vice versa. The dual of the dual code is always the original code.
Country calling codes, country dial-in codes, international subscriber dialing ( ISD) codes, or most commonly, telephone country codes are telephone number prefixes for reaching telephone subscribers in foreign countries or areas via international telecommunication networks. Country codes are defined by the International Telecommunication Union (ITU) in ITU-T standards E.123 and E.164. The ...
Electric generator. U.S. NRC image of a modern steam turbine generator (STG). In electricity generation, a generator [1] is a device that converts motion-based power ( potential and kinetic energy) or fuel-based power ( chemical energy) into electric power for use in an external circuit.
Linear code. In coding theory, a linear code is an error-correcting code for which any linear combination of codewords is also a codeword. Linear codes are traditionally partitioned into block codes and convolutional codes, although turbo codes can be seen as a hybrid of these two types. [1]
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 ...
Generator (mathematics) The 5th roots of unity in the complex plane under multiplication form a group of order 5. Each non-identity element by itself is a generator for the whole group. In mathematics and physics, the term generator or generating set may refer to any of a number of related concepts. The underlying concept in each case is that ...