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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.
Traditional Reed–Muller codes are binary codes, which means that messages and codewords are binary strings. When r and m are integers with 0 ≤ r ≤ m, the Reed–Muller code with parameters r and m is denoted as RM ( r , m ). When asked to encode a message consisting of k bits, where holds, the RM ( r , m) code produces a codeword ...
The International Chemical Identifier ( InChI, pronounced / ˈɪntʃiː / IN-chee) [ 3] is a textual identifier for chemical substances, designed to provide a standard way to encode molecular information and to facilitate the search for such information in databases and on the web. Initially developed by the International Union of Pure and ...
A chemical weapon agent (CWA), or chemical warfare agent, is a chemical substance whose toxic properties are meant to kill, injure or incapacitate human beings. About 70 different chemicals have been used or stockpiled as chemical weapon agents during the 20th century. These agents may be in liquid, gas or solid form.
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]
A chemical element, often simply called an element, is a type of atom which has a specific number of protons in its atomic nucleus (i.e., a specific atomic number, or Z). [ 1 ] The definitive visualisation of all 118 elements is the periodic table of the elements , whose history along the principles of the periodic law was one of the founding ...
Group code. In coding theory, group codes are a type of code. Group codes consist of linear block codes which are subgroups of , where is a finite Abelian group . A systematic group code is a code over of order defined by homomorphisms which determine the parity check bits. The remaining bits are the information bits themselves.