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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 code words. When code words 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 code word.

See also Code, Coding Theory, Error-Correcting Code, Gray Code, Huffman Coding, ISBN

© 1996-9 Eric W. Weisstein