Yes, you can. You can release your code however you want. The BSD license applies to the code provided by the project that chose to license their code under it. You can choose to also license your code as BSD, but you are not required to.
If I ignore or remove the BSD license from the 10 lines, I am removing the permission I had to use them.
Its like if I buy a train ticket. If I throw away the ticket and write my own, I no longer have permission to enter. The permission is in the ticket.
The 10 lines will must always be under the BSD, and every time I distribute I must follow the conditions set down by the license. It infects the distribution of the work, regardless of I license the other 100,000 lines.
