Unable to partition Internal Disk on El Capitan.

[imaginationrequired]

Hi there.

I'm trying to install Linux on my MacBook Air but seem to have fallen at the first hurdle and am unable to partition my disk. I open Disk Utility, I have ~70GB of free space and when I click partition at the top it starts the process.

What I then find is that Disk Utility says "Incorrect number of file hard links" and "Invalid directory item count", and then fails to partition the disk.

I have also tried to run first aid on my Macintosh HD, the same messages come up but then Disk Utility just says that the First Aid process is complete, leaving me still unable to create the partition.
Is there anyway I can fix this problem?

Thanks.

 

[richard2]

You should create a full backup of the contents of your internal disc in case it's failing. Once you've done that, try repairing the disc in recovery mode.