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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
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3 1 = 3 ≡ 3 (mod 5) 3 2 = 9 ≡ 4 (mod 5) 3 3 = 27 ≡ 2 (mod 5) 3 4 = 81 ≡ 1 (mod 5) Therefore, [3 4 2 1] is a Costas permutation. More specifically, this is an exponential Welch array. The transposition of the array is a logarithmic Welch array. The number of Welch–Costas arrays which exist for a given size depends on the totient function.
In linear algebra terms, the dual code is the annihilator of C with respect to the bilinear form . The dimension of C and its dual always add up to the length n : A generator matrix for the dual code is the parity-check matrix for the original code and vice versa. The dual of the dual code is always the original code.
Matrix digital rain. Matrix digital rain, or Matrix code, is the computer code featured in the Matrix series. The falling green code is a way of representing the activity of the simulated reality environment of the Matrix on screen by kinetic typography. All four Matrix movies, as well as the spin-off The Animatrix episodes, open with the code.
Download as PDF; Printable version ... Row Space Generator Matrix. As far as my understanding goes the linear code is the column space of the generator matrix, not ...
Vandermonde matrix. In linear algebra, a Vandermonde matrix, named after Alexandre-Théophile Vandermonde, is a matrix with the terms of a geometric progression in each row: an matrix. with entries , the jth power of the number , for all zero-based indices and . [1] Some authors define the Vandermonde matrix as the transpose of the above matrix.
Matrix-free methods. In computational mathematics, a matrix-free method is an algorithm for solving a linear system of equations or an eigenvalue problem that does not store the coefficient matrix explicitly, but accesses the matrix by evaluating matrix-vector products. [1] Such methods can be preferable when the matrix is so big that storing ...
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