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A generator matrix for a Reed–Muller code RM (r, m) of length N = 2m can be constructed as follows. Let us write the set of all m -dimensional binary vectors 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.).
Sphinx (documentation generator) Not to be confused with CMU Sphinx or Sphinx (search engine). Sphinx is a documentation generator written and used by the Python community. It is written in Python, and also used in other environments.
The matrix product of the generator and parity-check matrices, , is the matrix of all zeroes, and by intent. Indeed, this is an example of the very definition of any parity check matrix with respect to its generator matrix.
In mathematics and electronics engineering, a binary Golay code is a type of linear error-correcting code used in digital communications. The binary Golay code, along with the ternary Golay code, has a particularly deep and interesting connection to the theory of finite sporadic groups in mathematics. [1] These codes are named in honor of Marcel J. E. Golay whose 1949 paper [2] introducing ...
Parity-check matrix. In coding theory, a parity-check matrix of a linear block code C is a matrix which describes the linear relations that the components of a codeword must satisfy. It can be used to decide whether a particular vector is a codeword and is also used in decoding algorithms.
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 .
Free ( Mozilla Public License) an Office suite; allows to export (and import, with accuracy limitations) PDF files. Microsoft Word 2013. Proprietary. Desktop software. The 2013 edition of Office allows PDF files to be converted into a format that can be edited. Nitro PDF Reader. Freeware.