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This is a consequence of the fact that a parity check matrix of is a generator matrix of the dual code. G is a matrix, while H is a () matrix. Equivalent codes. Codes C 1 and C 2 are equivalent (denoted C 1 ~ C 2) if one code can be obtained from the other via the following two transformations: arbitrarily permute the components, and
The generator matrix. The Reed–Muller RM(r, m) code of order r and length N = 2 m is the code generated by v 0 and the wedge products of up to r of the v i, 1 ≤ i ≤ m (where by convention a wedge product of fewer than one vector is the identity for the
Games with available source code. The table below with available source code resulted not from official releases by companies or IP holders but from unclear release situations, like lost and found games, and leaks of unclear legality (e.g. by an individual developer on end-of-product-life) or undeleted content.
Most notably, Anonymous committed a cyberattack against Roskomnadzor. [214] March: On 23 March 2022, hackers compromised the Ronin Network, stealing approximately US$620 million in Ether and USDC. [215] [216] [217] A total of 173,600 Ether and 25.5 million USDC tokens were stolen in two transactions. [218]
Singleton bound. In coding theory, the Singleton bound, named after Richard Collom Singleton, is a relatively crude upper bound on the size of an arbitrary block code with block length , size and minimum distance . It is also known as the Joshibound. [1] proved by Joshi (1958) and even earlier by Komamiya (1953) .
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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 would write this in an equivalent form, cH ⊤ = 0.) The rows of a parity check matrix are the coefficients of the parity check equations.
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