CRC is an important error checking scheme used in network communication. Let G(x) = xk + ... + 1 be the divisor (also called generator polynomial), E(x) to be the error. CRC can detect following types of errors if the divisor G(x) satisfies specified conditions:

All single bit errors if k >=1 and coefficient of x is not zero.

All double bits errors if G(x) has at least three terms

All odd number of bits errors if G(x) has a factor of x+1

Any burst errors of length =k

Consider a CRC with G(x) = x + x + x + 1, (k=4). What kind of errors can be detected by this given G(x)?