Often in coding theory, a code's alphabet is taken to be a finite field. In particular, if $A$ is the finite field with two (resp. three, four, etc.) elements, we call $C$ a binary (resp. ternary, quaternary, etc.) code. In particular, when our alphabet is a finite field then the set $A^n$ is a vector space over $A$ and we define a <</SPAN>#108#>linear code over $A$ of block length $n$ to be a subspace (as opposed to merely a subset) of $A^n$ We define the <</SPAN>#109#>dimension of $C$ to be its dimension as a vector space over $A$

Though not sufficient for unique classification, a linear code's block length, dimension, and minimum distance are three crucial parameters in determining the strength of the code. For referencing, a linear code with block length $n$ dimension $k$ and minimum distance $d$ is referred to as an $(n,k,d)$ code.

Some examples of linear codes are Hamming Codes, BCH codes, Goppa codes, Reed-Solomon codes, and the Golay code.