Disclaimer: I am not a lawyer, and this answer does not constitute legal advice.
You can submit your new version to MATLAB exchange, or distribute your code in any other way that you wish, as long as the original BSD license is distributed with it. I recommend that you read the BSD license itself. The page you linked to clearly states: Do I have to ask an author's permission to use BSD-licensed code?
No. Permission to use the code is granted in the license.
Do I have to acknowledge the author of code I'm reusing?
No, but you do have to keep the original BSD license attached to the code and include it with any derivative work you create.
So this means that you can do whatever changes you want, and then post your (derivative) work on FEX, and all you have to do is to include the original license together with your distribution (note that FEX only supports BSD licensing). In practice many people simply add their own name and year (of modification) to the original BSD license, something like this:
Copyright (c) 1985, Anna Smith
Copyright (c) 2016, Pasc Peli
All rights reserved.
etc
MATLAB FEX also provides a field where you can list other FEX submissions that you have included in your own submission, but while this might be a nice thing to do it is not required by the BSD license.
Best Answer