After updating to iOS 6.1 on iphone 5 have no connection

Hi,

After I installed iOS 6.1 on my Iphone 5, I have no connection as it shows "no service".  I can connect to WiFi.  Even after putting the phone on Airplane mode ON and waiting a while before swiching back to OFF it says searching and after a couple of seconds it shows "no service".  I have done a hard reset and when the phone comes on, I have full signal strenght and 3G connection for 2 or so minutes.  After I made a call after a hard reset the phone goes back to "no service".

I have checked to make sure it is not the service provider as this occurs at different locations.

Any suggestions?