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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.).
A product key, also known as a software key, serial key or activation key, is a specific software-based key for a computer program. It certifies that the copy of the program is original. Product keys consist of a series of numbers and/or letters. This sequence is typically entered by the user during the installation of computer software, and is ...
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.
Microsoft Product Activation is a DRM technology used by Microsoft Corporation in several of its computer software programs, most notably its Windows operating system and its Office productivity suite. The procedure enforces compliance with the program's end-user license agreement by transmitting information about both the product key used to ...
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]
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Keygen. A key generator ( key-gen) is a computer program that generates a product licensing key, such as a serial number, necessary to activate for use of a software application. Keygens may be legitimately distributed by software manufacturers for licensing software in commercial environments where software has been licensed in bulk for an ...
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