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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.).
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 ...
Key generator. A key generator [1] [2] [3] is a protocol or algorithm that is used in many cryptographic protocols to generate a sequence with many pseudo-random characteristics. This sequence is used as an encryption key at one end of communication, and as a decryption key at the other. One can implement a key generator in a system that aims ...
Software cracking (known as "breaking" mostly in the 1980s [ 1]) is an act of removing copy protection from a software. [ 2] Copy protection can be removed by applying a specific crack. A crack can mean any tool that enables breaking software protection, a stolen product key, or guessed password. Cracking software generally involves ...
The attacker knows ^, the generator matrix of an (,) code ^ that is combinatorially able to correct errors. The attacker may ignore the fact that C ^ {\displaystyle {\hat {C}}} is really the obfuscation of a structured code chosen from a specific family, and instead just use an algorithm for decoding with any linear code.
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 ...
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.
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]