[[2,10],[6,6]]-equitable partitions of the 12-cube

We describe the computer-aided classification of equitable partitions of the 12-cube with quotient matrix [[2,10],[6,6]], or, equivalently, simple orthogonal arrays OA(1536,12,2,7), or order-7 correlation-immune Boolean functions in 12 variables with 1536 ones (which completes the classification of unbalanced order-7 correlation-immune Boolean functions in 12 variables). We find that there are 103 equivalence classes of the considered objects, and there are only two almost-OA(1536,12,2,8) among them.