Optimal (v, 3, 1) binary cyclically permutable constant weight codes with small v

We classify up to multiplier equivalence optimal (v, 3, 1) binary cyclically permutable constant weight (CPCW) codes with v ≤ 61. There is a one-to-one correspondence between optimal (v, 3, 1) CPCW codes, optimal cyclic binary constant weight codes with weight 3 and minimal distance 4, (v, 3; b(v − 1)/6c) difference packings, and optimal (v, 3, 1) optical orthogonal codes. Therefore the classification of CPCW codes holds for them too. Some of the classified (v, 3, 1) CPCW codes are perfect and they are equivalent to cyclic Steiner triple systems of order v (STS(v)) and (v, 3, 1) cyclic difference families. This way we obtain a classification of cyclic STS(61) and (61, 3, 1) cyclic difference families which is new.