Binary cyclic codes of length seven
= Binary cyclic codes of length seven
Over $\mathbb F_2$,
$$
X^7-1=(X+1)(X^3+X+1)(X^3+X^2+1).
$$
Its eight monic divisors generate the eight cyclic codes of length seven: the whole-space, even-weight, two Hamming, two simplex, repetition, and zero codes.