Content deleted Content added
DavidCBryant (talk | contribs) →Popular notation: Regularized in-line expressions and clarified the prose. Long parentheticals interfere with ellipsis, imo. |
m →Formal definition: fmt |
||
Line 3:
==Formal definition==
A '''linear code''' of length ''n'' and rank ''k'' is a [[linear subspace]] ''C'' with [[dimension (linear algebra)|dimension]] ''k'' of the [[vector space]] <math>\mathbb{F}_q^n</math> where <math>\mathbb{F}_q</math> is the [[finite field]] with ''q'' elements. Such a code with parameter ''q'' is called a ''q''-ary code (e.g., when ''q'' = 5, the code is a 5-ary code). If ''q'' = 2 or ''q'' = 3, the code is described as a '''binary code''', or a '''ternary code'''.
==Properties==
| |||