Almost difference families (ADFs) were introduced by Ding and Yin as an useful generalization of almost difference sets (ADSs), and a number of infinite classes of almost difference families had been constructed. In this note, we improve the results of the existence of cyclic -ADFs and establish three results of the existence of cyclic -ADFs.
Research supported by the National Natural Science Foundation of China under Grant No. 10971252, the Scientific-Technological Project of Nantong City under Grant No. K2009036, and the Program for the Innovation Talents of Nantong University.