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This is a consequence of the fact that a parity check matrix of is a generator matrix of the dual code. G is a matrix, while H is a () matrix. Equivalent codes. Codes C 1 and C 2 are equivalent (denoted C 1 ~ C 2) if one code can be obtained from the other via the following two transformations: arbitrarily permute the components, and
Specific Area Message Encoding (SAME) is a protocol used for framing and classification of broadcasting emergency warning messages. It was developed by the United States National Weather Service for use on its NOAA Weather Radio (NWR) network, and was later adopted by the Federal Communications Commission for the Emergency Alert System, then subsequently by Environment Canada for use on its ...
Formally, a parity check matrix H of a linear code C is a generator matrix of the dual code, C ⊥. This means that a codeword c is in C if and only if the matrix-vector product Hc ⊤ = 0 (some authors would write this in an equivalent form, cH ⊤ = 0.) The rows of a parity check matrix are the coefficients of the parity check equations.
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Systematic code. In coding theory, a systematic code is any error-correcting code in which the input data are embedded in the encoded output. Conversely, in a non-systematic code the output does not contain the input symbols. Systematic codes have the advantage that the parity data can simply be appended to the source block, and receivers do ...
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.
See the ISO 3166-3 standard for former country codes. British Virgin Islands – See Virgin Islands (British) . Burma – See Myanmar . Cape Verde – See Cabo Verde . Caribbean Netherlands – See Bonaire, Sint Eustatius and Saba . China, The Republic of – See Taiwan (Province of China) . Democratic People's Republic of Korea – See Korea ...