Build a context-free grammar for a context-free language A context-free language is defined by its description:

$L=(a^{2k} \space  b^n \space c^{2n} \mid k \geq 0, \space n &gt; 0)$

For example:

$bcc, aabcc, aabbcccc, bbcccc$

How to build a context-free grammar for this context-free language?

I suppose that the order for generating any chain in this problem matters: 'b' will always stand after 'a' and 'c' - after 'b'. Is it so?

My attempts leaded to this solution:

$ S \rightarrow aaAbcc \mid bAcc \mid aabAcc $

$ A \rightarrow aa \mid bcc \mid λ $

Please correct me if I'm wrong or better offer your solution to this problem.
$ S \rightarrow EG $ , 
$ E \rightarrow aO \mid λ $ ,
$ O \rightarrow aE $ ,
$ F \rightarrow bFcc \mid λ $, 
$ G \rightarrow bFcc $ .
I am assuming $λ$ stands for empty string.

Better one:

$ S \rightarrow EF $ , 
$ E \rightarrow aO \mid λ $ ,
$ O \rightarrow aE $ ,
$ F \rightarrow bFcc \mid bcc $.