Often in coding , a code’s alphabet is taken to be a finite field. In particular, if is the finite field with two (resp. three, four, etc.) elements, we call a binary (resp. ternary, quaternary, etc.) code. In particular, when our alphabet is a finite field then the set is a vector space over , and we define a linear code over of block length to be a subspace (as opposed to merely a subset) of . We define the dimension of to be its dimension as a vector space over .
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 , dimension , and minimum distance is referred to as an -code.
|Date of creation||2013-03-22 14:21:24|
|Last modified on||2013-03-22 14:21:24|
|Last modified by||mathcam (2727)|
|Defines||dimension of a linear code|