Optimal (v, 4, 1) binary cyclically permutable constant weight codes ((v,4,1) optical orthogonal codes (OOC)) and cyclic S(2, 4, v) designs

All (v,4,1) OOC for:

1) 26≤v≤68

2) v=69

3) v=70

4) v=71

5) v=72

6) 73≤v≤76

7) v=85a, v=85b, v=85c

Not all (v,4,1) OOC. The codes below are constructed by backtrack search, but only the first 3 possibilities for the n-th codeword (n > 1) are considered (at most 3 branches)

1) 77≤v≤98

Not all (v,4,1) OOC. The codes below are constructed by backtrack search, but only the first 2 possibilities for the n-th codeword (n > 1) are considered (at most 2 branches)

1) 99≤v≤107

2) 108≤v≤117

3) 118≤v≤127

4) 128≤v≤131

5) v=132

6) 133≤v≤136

All cyclic 2-(v,4,1) designs

1) v=40, 52, 64, 76

2) v=88

Not all cyclic 2-(v,4,1) designs. The designs below are constructed by backtrack search, but only the first 2 possibilities for the n-th baseblock (n > 1 for strictly cyclic designs, n>2 for designs with one short orbit) are considered (at most 2 branches)

1) 100≤v≤160