Can I secure my code from being copied on arduino boards?

Atmel AVR231: AES Bootloader
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This application note describes how firmware can be updated securely on AVR
microcontrollers with bootloader capabilities. The method uses the Advanced
Encryption Standard (AES) to encrypt the firmware.

This application note presents techniques that can be used when securing a design
from outside access. Although no design can ever be fully secured it can be
constructed such that the effort required to break the security is as high as possible.
There is a significant difference between an unsecured design that a person with
basic engineering skills can duplicate and a design that only few, highly skilled
intruders can break. In the unsecured case, the design is easily copied and even
reverse engineered, violating the intellectual property of the manufacturer and
jeopardizing the market potential for the design. In the secured case, the effort
required to break the design is so high that most intruders simply focus on developing
their own products.