Changing location of core dump

Yes, it is. You can change /proc/sys/kernel/core_pattern to define the pathname used to generate the corefile. For more, see man core

example:

echo '/tmp/core_%e.%p' | sudo tee /proc/sys/kernel/core_pattern    # `tee' instead of > so that
                                                                   # opening happens in the
                                                                   # elevated process

would cause all future core dumps to be generated in /tmp and be named core_[program].[pid]