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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.
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.).
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
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Schematic depiction of a concatenated code built upon an inner code and an outer code. This is a pictorial representation of a code concatenation, and, in particular, the Reed–Solomon code with n=q=4 and k=2 is used as the outer code and the Hadamard code with n=q and k=log q is used as the inner code. Overall, the concatenated code is a -code.
A 2011 Comic-Con poster depicting many characters from the first season. This is a list of characters from My Little Pony: Friendship Is Magic, an animated television series based on the My Little Pony toyline created by American toy manufacturer and multimedia company Hasbro. The series features characters and settings developed by Lauren Faust, who sought to create more in-depth characters ...
Contents. List of The Nightmare Before Christmas characters. From left to right: Doctor Finkelstein, the Mayor, Sally, Jack, Barrel, Santa Claus, Zero, Lock, Shock and Oogie Boogie. This article lists characters seen in the film The Nightmare Before Christmas and the video games The Nightmare Before Christmas: The Pumpkin King and The Nightmare ...