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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 ...
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, 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 Animatrix episodes, open ...
The RadioShack TRS-80 Color Computer, later marketed as the Tandy Color Computer, is a series of home computers developed and sold by Tandy Corporation.Despite sharing a name with the earlier TRS-80, the Color Computer is a completely different system and a radical departure in design based on the Motorola 6809E processor rather than the Zilog Z80 of earlier models.
The first element of a CIRC decoder is a relatively weak inner (32,28) Reed–Solomon code, shortened from a (255,251) code with 8-bit symbols. This code can correct up to 2 byte errors per 32-byte block. More importantly, it flags as erasures any uncorrectable blocks, i.e., blocks with more than 2 byte errors.
element .io. Element (formerly Riot and Vector[ 11]) is a free and open-source software instant messaging client implementing the Matrix protocol. [ 12] Element supports end-to-end encryption, [ 13] private and public groups, sharing of files between users, voice and video calls, and other collaborative features with help of bots and widgets.
The distance of the concatenated code Cout ∘ Cin is at least dD, that is, it is a [ nN, kK, D '] code with D ' ≥ dD . Proof: Consider two different messages m1 ≠ m2 ∈ BK. Let Δ denote the distance between two codewords. Then. Thus, there are at least D positions in which the sequence of N symbols of the codewords Cout ( m1) and Cout ...
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]