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Linear Code


A linear code over a finite field with q elements F_q is a linear subspace C subset F_q^n. The vectors forming the subspace are called codewords. When codewords are chosen such that the distance between them is maximized, the code is called error-correcting since slightly garbled vectors can be recovered by choosing the nearest codeword.


See also

Code, Coding Theory, Error-Correcting Code, Gray Code, Huffman Coding, ISBN, UPC

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Cite this as:

Weisstein, Eric W. "Linear Code." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LinearCode.html

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