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

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 26≤v≤76 and v=85: All_oc_26-85_4_1.zip All cyclic 2-(v,4,1) designs for v=40, 52, 64, 76, 88: d_4_1.zip. Some (v,4,1) OOC: The codes are constructed by backtrack search considering all possibilities for the first two codewords (n=0 and n=1), but only the first 3 possibilities for the n-th codeword (n > 1) are considered for 77≤v≤98: E3oc_77-98_4_1.zip. The codes are constructed by backtrack search considering all possibilities for the first two codewords (n=0 and n=1), but only the first 2 possibilities for the n-th codeword (n > 1) are considered for 99≤v≤136: E2oc_99-136_4_1.zip Some cyclic 2-(v,4,1) designs. The designs are constructed by backtrack search considering all possibilities for the first two or three baseblocks, 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 for 100≤v≤160: E2d_4_1.zip