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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.
Roblox ( / ˈroʊblɒks / ROH-bloks) is an online game platform and game creation system developed by Roblox Corporation that allows users to program and play games created by themselves or other users. Created by David Baszucki and Erik Cassel in 2004 and released in 2006, the platform hosts user-created games of multiple genres coded in the programming language Lua. For most of Roblox ' s ...
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 .
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Reed–Muller codes generalize the Reed–Solomon codes and the Walsh–Hadamard code. 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 .
Reports of American consumers’ inability to pay their bills—or their waning interest in shopping—are greatly exaggerated.
Karen Read is charged with second-degree murder in the January 2022 death of Boston Police Officer John O’Keefe. Lally reminded jurors that four witnesses reported hearing Read say those words ...
A linear code of length n and dimension k is a linear subspace C with dimension k of the vector space where is the finite field with q elements. Such a code is called a q -ary code. If q = 2 or q = 3, the code is described as a binary code, or a ternary code respectively. The vectors in C are called codewords. The size of a code is the number of codewords and equals qk .