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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.).
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Welcome to Bloxburg is a life-simulation and role-playing game created in 2014. [121] The game is based on The Sims, and is noted for being a Roblox game in which players had to purchase 25 Robux before playing. [122] It was acquired by Embracer Group in 2023 under Coffee Stain Gothenburg, [a] a subsidiary of Coffee Stain created for Bloxburg.
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]
Biles’ age is already advanced for this sport — she’s the oldest American female Olympic gymnast since the 1950s. Yet she doesn’t sound like someone who is ready to leave the sport.
A car built by the Orange County Choppers trio of Mikey, Paul Jr, and Paul Teutul Sr. and powered by AOL's 9.0 Top Speed technology, sends Mikey back to the Renaissance. AOL "Motorcycle" Mikey, Paul Jr, and Paul Sr. build a chopper that runs on AOL's 9.0 Top Speed Speed technology. The trio attempts to jump the bike over a row of cement trucks ...
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.
Group code. In coding theory, group codes are a type of code. Group codes consist of linear block codes which are subgroups of , where is a finite Abelian group . A systematic group code is a code over of order defined by homomorphisms which determine the parity check bits. The remaining bits are the information bits themselves.