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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.).
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 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.
The distance of the concatenated code Cout ∘ Cin is at least dD, that is, it is a [ nN, kK, D '] code with D ' ≥ dD . Proof: Consider two different messages m1 ≠ m2 ∈ BK. Let Δ denote the distance between two codewords. Then. Thus, there are at least D positions in which the sequence of N symbols of the codewords Cout ( m1) and Cout ...
HTML is a markup language that defines the structure and presentation of web pages. It is one of the core technologies of the World Wide Web, along with CSS and JavaScript. HTML allows creating and formatting text, images, links, tables, forms, and other elements on a web page. Learn more about the history, syntax, and features of HTML on Wikipedia.
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]
CSS HTML Validator (previously named CSE HTML Validator) is an HTML editor and CSS editor for Windows (and Linux when used with Wine) that helps web developers create syntactically correct and accessible HTML / HTML5, XHTML, and CSS documents by locating errors, potential problems like browser compatibility issues, and common mistakes.
W3Schools is a freemium educational website for learning coding online. [ 1][ 2] Initially released in 1998, it derives its name from the World Wide Web but is not affiliated with the W3 Consortium. [ 3][ 4][unreliable source] W3Schools offers courses covering many aspects of web development. [ 5] W3Schools also publishes free HTML templates.