This is related to some other questions, such as: this, and some of my other questions.
In this question, and others, we see we can declare and initialise string arrays
The reason you can't declare your array like that (const char* []) is that:
const char* []
does not state how much space the compiler needs to allocate for each instance (your array is declared as instance variable).Besides, you probably want to make that array static, since it is in essence a constant value.