Finding all vectors that correlate to each other

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Given an $\text{n-dimensional}$ space, a sparse binary vector in that space and a product value

(for example $n=6$, $\vec{v}=(1, 1, 1, 0, 0, 0)$, and inner=1)

I would like to find all other binary vectors in that space that have the same norm and all share the same inner product to one another.

for example,$\vec{v}$, I would like to find the set of binary vectors with $6$ components with only 3 values of 1, which all have an inner product of 1 to each other. these following vectors are included in that set:

$\vec{v_1}=(1, 1, 1, 0, 0, 0)$

$\vec{v_2}=(1, 0, 0, 0, 1, 1)$

$\vec{v_3}=(0, 0, 1, 1, 1, 0)$

all of these have only 3 values of 1, and all of the inner products of vectors in the set are the same as our inner_product, 1.

Thank you very much!