It's impossible to give access to parts of a file to a certain group of users.
It seems that you need to rethink your security policies. What is in the sections of the file that you don't want most people to see? Perhaps it's not appropriate for that information to be in the file at all?
The most obvious approach to fixing this is to remove the secret code from the file and to store it in a separate module. You can then adjust the permissions of the module so that only the correct people can see it.
It is, however, important to note that a user needs to be able to read a file in order to execute that file. If a particular user cannot read a module that is required by a program, then that user will not be able to run that program.
This is a restriction that is inherent in programming languages like Perl where there is no "compiled" version of the code that you can share. People need to be able to read the source code in order to run the program.
If that's a problem for you, then perhaps Perl is not the right language for this project.