Optimal ternary constant-composition codes with weight four and distance three

Abstract A concept of good overlarge set of disjoint packing triple systems (OLPTS) is introduced in order to characterize a ternary constant-composition code with weight four, distance three and the composition [ 3 , 1 ] . A recursive construction for good OLPTSs via fan designs is also given. 4-cycle free one-factorizations of the complete graphs are also used to construct optimal ternary constant-composition codes with weight four distance three and the composition [ 2 , 2 ] . Consequently, a few infinite classes of optimal ternary constant-composition codes with weight four and distance three are obtained.