It depends on which of two compression schemes Windows used.
If your file was compressed to a .zip file:
Start a command shell
cd to the directory where you put the compressed blend file (it might be named something like “myfile.blend.zip”)
Enter the command unzip myfile.blend.zip.
If it is NTFS compression (the filename does not end in .zip)
Then you are out of luck, I think. I know there are people working on NTFS data in linux, but Microsoft is not helping them at all so the pickings are currently fairly slim. Go back to windows and get a copy of the file uncompressed and copy that to linux.
Ah, I had never noticed that feature before. So you selected ‘enable file compression’ on your Linux blender and then opened the file without any trouble, right?
Blender compresses the file with gzip compression inside a .blend file. If you still can’t get it to work after you try the previous method, try the way I said.