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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.).
The Hadamard code is a linear code, and all linear codes can be generated by a generator matrix .This is a matrix such that () = holds for all {,}, where the message is viewed as a row vector and the vector-matrix product is understood in the vector space over the finite field.
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 [1] would write this in an equivalent form, cH ⊤ = 0.) The rows of a parity check matrix are the coefficients of the parity check equations. [2]
Convolutional code. In telecommunication, a convolutional code is a type of error-correcting code that generates parity symbols via the sliding application of a boolean polynomial function to a data stream. The sliding application represents the 'convolution' of the encoder over the data, which gives rise to the term 'convolutional coding'.
In mathematical terms, Hamming codes are a class of binary linear code. For each integer r ≥ 2 there is a code-word with block length n = 2r − 1 and message length k = 2r − r − 1. Hence the rate of Hamming codes is R = k / n = 1 − r / (2r − 1), which is the highest possible for codes with minimum distance of three (i.e., the minimal ...
C/C++, C#, D, IDL, Fortran, Java, PHP, Python Any 1997/10/26 1.9.1 GPL Epydoc: Edward Loper Text Python Any 2002/01/— 3.0 (2008) MIT: fpdoc (Free Pascal Documentation Generator) Sebastian Guenther and Free Pascal Core Text (Object)Pascal/Delphi FPC tier 1 targets 2005 3.2.2 GPL reusable parts are GPL with static linking exception Haddock ...
A chart of accounts ( COA) is a list of financial accounts and reference numbers, grouped into categories, such as assets, liabilities, equity, revenue and expenses, and used for recording transactions in the organization's general ledger. Accounts may be associated with an identifier (account number) and a caption or header and are coded by ...
To do so technically would require a more sophisticated grammar, like a Chomsky Type 1 grammar, also termed a context-sensitive grammar. However, parser generators for context-free grammars often support the ability for user-written code to introduce limited amounts of context-sensitivity. (For example, upon encountering a variable declaration ...