Properties
Over GF(2) the AOP has many interesting properties, including:
- The Hamming weight of the AOP is m + 1
- The AOP is irreducible if and only if m + 1 is prime and 2 is a primitive root modulo m + 1
- The only AOP that is a primitive polynomial is x2 + x + 1.
Despite the fact that the Hamming weight is large, because of the ease of representation and other improvements there are efficient implementations in areas such as coding theory and cryptography.
Over, the AOP is irreducible whenever m + 1 is prime p, and therefore in these cases, the pth cyclotomic polynomial.
Read more about this topic: All One Polynomial
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