Non primitive lfsr sequence

Given a non-primitive LFSR sequence (i.e number of states is less than $2^n - 1$); how do we find out the the characteristic polynomial? Will Berlekamp-Massey algorithm work in this case?

for example; for the following sequence-

[1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1]

the repetition period is $105$. Applying the Berlekamp-Massey algorithm returns

$X^7 + X^6 + X^5 + X^1 + 1$

Doing manually gives me a different answer. Where am I going wrong?

EDIT

I found the primitive polynomials and took LCM to confirm the $Berlekamp-Massey$ output.

To check, I represented the polynomial as $11100011$ ; took the first seven bits of the sequence and did the $and$ operation with the polynomial. took the $xor$ of the output and appended that output to the initial 7 bits and continued. This is what I did to crosscheck the answer I received. It is here I went wrong probably.

A binary sequence of period $105$ will have characteristic polynomial that is a divisor of $x^{105}-1$. Since $x^{105}-1$ has irreducible factors of degrees $12, 4, 3$, and $1$, it is possible to have an LFSR of length $4+3=7$ generate a sequence of period $105$, and that is exactly what has happened here. Note that $$x^7+x^6+x^5+x+1 = (x^3+x+1)(x^4+x^3+1)$$ where $x^3+x+1$ and $x^4+x^3+1$ are irreducible (in fact, primitive) polynomials of degrees $3$ and $4$. Individually, the shorter LFSRs generate sequences of periods $7$ and $15$: the "product" sequence has period $\operatorname{lcm}(7,15)=105$.