...but need the help of you folks.

I read some stuff about bitcoin but I can't answer this myself.

Is the bitcoin protocol intrinsically linked to bitcoin mining?

Or in other words, could I come up with something totally different as mining algorithm and still be using the bitcoin protocol to disseminate newly created coins? I am perfectly aware that these would not be genuine bitcoins, and in fact, they don't need to be. It would be some kind of a fork.

My gut feeling tells me it's all "one", an interrelated stack. And probably, my idea of how to generate new coins cannot possibly be as secure and robust as bitcoin is, if at all possible, but it would be wonderful if it could, and that's why I am trying this forum with the experts.

In short: generating coins in a different way but divulgate through the network, is that possible?
Thanks