Need an Introduction to Tiny Core? Or peruse Core Concepts.
The linux kernel itself requires > 4mb ram.
I would not consider to run Linux an any Cortex Mx chips. There are nice alternatives like MicroPython, various RTOS's, etc.It may worth to read:https://electronics.stackexchange.com/questions/27594/what-operating-systems-have-been-ported-to-cortex-m3