My AVG program gave me a warning notice that malware had been detected and asked that I immediately turn my computer off. I did that and then restarted again. AVG said they had deleted SynCore11.exe. I was not familiar with this but found out it is a part of SoundMax. Now some of my programe wont start and the message given is "Unable to find or execute SynthCore11.exe". Can this now be reinstalled? What was the connection with malware? How can this be fixed?

I find it odd it told you to turn off you computer. That normally is not a good idea because then malicious code could be installed during the next boot before your security software is able to load.

If me, I scan with your AVG again. And verify with Malwarebytes's Anti-Malware (MBAM). Then if you uninstall your sound drivers and reinstall them, it should fix your problem. You should be able to get new drivers from your motherboard or computer makers website.