Classification of optimal (v,k,1) binary cyclically permutable constant weight codes with k=5,6 and 7 and small lengths

摘要

We classify optimal (v,k,1) binary cyclically permutable constant weight (CPCW) codes with small v and k=5,6 and 7. Binary CPCW codes have multiple applications in contemporary communications and are closely related to cyclic binary constant weight codes, difference packings, optical orthogonal codes, cyclic difference families and cyclic block designs. The presented small length codes can be used in relevant applications, as well as with recursive constructions for bigger lengths. We also establish that a (127,7,1) cyclic difference family does not exist.