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It is well known that fast correlation attacks can be very efficient if the feedback polynomial is of low weight. These feedback polynomials can be considered weak in the context of stream ciphers. This paper generalizes the class of weak feedback polynomials into polynomials were taps are located in several groups, possibly far apart. Low-weight feedback polynomials are thus a special case of this class. For the general class, it is shown that attacks can sometimes be very efficient even though the polynomials are of large weight. The main idea is to consider vectors of noise variables. It is shown how the complexity of a distinguishing attack can be efficiently computed and that the complexity is closely related to the minimum row distance of a generator matrix for a convolutional code. Moreover, theoretical results on the size of the vectors are given.