A linear code over a finite field with 
elements 
is a linear subspace 
. 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.
Linear Code
See also
Code, Coding Theory, Error-Correcting Code, Gray Code, Huffman Coding, ISBN, UPCExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Linear Code." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LinearCode.html