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In coding theory, a generator matrix is a matrix whose rows form a basis for a linear code. The codewords are all of the linear combinations of the rows of this matrix, that is, the linear code is the row space of its generator matrix.
Reed–Muller codes are linear block codes that are locally testable, locally decodable, and list decodable. These properties make them particularly useful in the design of probabilistically checkable proofs . Traditional Reed–Muller codes are binary codes, which means that messages and codewords are binary strings.
Roblox is free to play, with in-game purchases available through a virtual currency called Robux. As of August 2020, Roblox had over 164 million monthly active users, including more than half of all American children under 16. [12] [13] Although Roblox has received generally positive reviews from critics, it has faced criticism for its moderation, microtransactions, and allegations of ...
LDPC codes have been shown to have ideal combinatorial properties. In his dissertation, Gallager showed that LDPC codes achieve the Gilbert–Varshamov bound for linear codes over binary fields with high probability. In 2020 it was shown that Gallager's LDPC codes achieve list decoding capacity and also achieve the Gilbert–Varshamov bound for linear codes over general fields. [9]
Parity-check matrix. In coding theory, a parity-check matrix of a linear block code C is a matrix which describes the linear relations that the components of a codeword must satisfy. It can be used to decide whether a particular vector is a codeword and is also used in decoding algorithms.
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.
Becoming a millionaire within a decade may sound like a pipe dream, but The Ramsey Show co-host George Kamel made it happen.
Pastebin. A pastebin or text storage site [1] [2] [3] is a type of online content-hosting service where users can store plain text (e.g. source code snippets for code review via Internet Relay Chat (IRC)). The most famous pastebin is the eponymous pastebin.com. [citation needed] Other sites with the same functionality have appeared, and several ...