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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.).
Matrix digital rain. Matrix digital rain, or Matrix code, is the computer code featured in the “Ghost in the shell” and 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 ...
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 ...
Barcode. A UPC-A barcode. A barcode or bar code is a method of representing data in a visual, machine-readable form. Initially, barcodes represented data by varying the widths, spacings and sizes of parallel lines. These barcodes, now commonly referred to as linear or one-dimensional (1D), can be scanned by special optical scanners, called ...
A Data Matrix is a two-dimensional code consisting of black and white "cells" or dots arranged in either a square or rectangular pattern, also known as a matrix. The information to be encoded can be text or numeric data. Usual data size is from a few bytes up to 1556 bytes. The length of the encoded data depends on the number of cells in the ...
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.
Bane. Bane (played by Ian Bliss) is a crew member of the Zion hovercraft Caduceus in the films The Matrix Reloaded and The Matrix Revolutions. His consciousness is overwritten by Smith in the Matrix, allowing Smith to take control of Bane in the real world. He attempts to assassinate Neo, but is foiled by the Kid.
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]