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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 ...
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 ...
1 Control-C has typically been used as a "break" or "interrupt" key. 2 Control-D has been used to signal "end of file" for text typed in at the terminal on Unix / Linux systems. Windows, DOS, and older minicomputers used Control-Z for this purpose. 3 Control-G is an artifact of the days when teletypes were in use.
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 ...
Users can use Midjourney through Discord either through their official Discord server, by directly messaging the bot, or by inviting the bot to a third-party server. To generate images, users use the /imagine command and type in a prompt; [ 22 ] the bot then returns a set of four images, which users are given the option to upscale .
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]
Mathematical definition. In mathematical terms, the extended binary Golay code G24 consists of a 12-dimensional linear subspace W of the space V = F24. 2 of 24-bit words such that any two distinct elements of W differ in at least 8 coordinates. W is called a linear code because it is a vector space. In all, W comprises 4096 = 212 elements.