Seven infinite classes of relative difference families with variable block sizes are presented explicitly. In particular, a balanced ( gv , g , K ,1)-DF with  g =Σ k∈K [( k  2 - k )/2] is explicitly given for: (i)  K ={3,4,5} and every  v  coprime to 6; (ii)  K ={3,4,6}, {3,5,6} or {3,4,5,6} and every  v  coprime to 30. As far as the authors are aware, these difference families can be viewed as the first explicit constructions of infinite classes of optimal variable-weight optical orthogonal codes with more than two weights. It is observed, however, that there are infinitely many values of  v  for which an optimal ( v , W ,1, Q ) -OOC exists, whatever the set of weights  W  and the weight distribution sequence  Q  are.
['Marco Buratti', 'Yueer Wei', 'Dianhua Wu', 'Pingzhi Fan', 'Minquan Cheng']
Relative Difference Families With Variable Block Sizes and Their Related OOCs