Note
A note on cyclic almost difference families

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Abstract

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 (q,6,λ,t)-ADFs and establish three results of the existence of cyclic (q,7,λ,t)-ADFs.

Keywords

Almost difference family
Difference family
Almost difference set
Cyclotomic class

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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.