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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.).
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 ...
The cheaper filter material used in the monochromatic past dictated red and blue for convenience and cost. There is a material improvement of full color images with the cyan filter, especially for accurate skin tones. Video games, theatrical films, and DVDs can be shown in the anaglyph 3D process.
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]
The Hadamard code is a linear code, and all linear codes can be generated by a generator matrix . This is a matrix such that Had ( x ) = x ⋅ G {\displaystyle {\text{Had}}(x)=x\cdot G} holds for all x ∈ { 0 , 1 } k {\displaystyle x\in \{0,1\}^{k}} , where the message x {\displaystyle x} is viewed as a row vector and the vector-matrix product ...
Linear code. In coding theory, a linear code is an error-correcting code for which any linear combination of codewords is also a codeword. Linear codes are traditionally partitioned into block codes and convolutional codes, although turbo codes can be seen as a hybrid of these two types. [1] Linear codes allow for more efficient encoding and ...
Safety glass is glass with additional safety features that make it less likely to break, or less likely to pose a threat when broken. Common designs include toughened glass (also known as tempered glass), laminated glass, and wire mesh glass (also known as wired glass). Toughened glass was invented in 1874 by Francois Barthelemy Alfred Royer de ...
Glasses. Glasses, also known as eyeglasses and spectacles, are vision eyewear with clear or tinted lenses mounted in a frame that holds them in front of a person's eyes, typically utilizing a bridge over the nose and hinged arms, known as temples or temple pieces that rest over the ears. Glasses are typically used for vision correction, such as ...