There are just so many things that could've factored into this happening - Impossible to speculate about your options. Best way to find it out is to file for unemployment. I remember several years ago, a past employer hadn't been very careful in documenting all the steps they took before firing....And the employee was more or less able to come back though in a different position. If your employer has enough documentation; thing like:
Tardy or excessive absence
Negative performance reviews
Negative customer input
Fraud...Or not being found to be completely truthful or ethical in your professional capacity (calling in sick when you weren't. saying you completed a task when you didn't)
Then they can fire you. If you had only worked there for X months, then you also fall under "at will" and they can fire you without cause.
Another option employers can use, is "reorganization" which basically means, it is not so much that they fired you but that they eliminated or significantly changed your position. Very little recourse for you in such a situation.
The other issue at hand is that you are talking about something that happened in October. I assume you have filed for unemployment? If so, your case was probably at least marginally reviewed and found to be reasonable.