  Pseudorandom binary sequences with optimal balance and autocorrelation have
many applications in stream cipher, communication, coding theory, etc. It is
known that binary sequences with three-level autocorrelation should have an
almost difference set as their characteristic sets. How to construct new
families of almost difference set is an important research topic in such fields
as communication, coding theory and cryptography. In a work of Ding, Helleseth,
and Martinsen in 2001, the authors developed a new method, known as the
Ding-Helleseth-Martinsens Constructions in literature, of constructing an
almost difference set from product sets of GF(2) and the union of two
cyclotomic classes of order four. In the present paper, we have constructed two
classes of almost difference set with product sets between GF(2) and union sets
of the cyclotomic classes of order 12 using that method. In addition, we could
find there do not exist the Ding-Helleseth-Martinsens Constructions for the
cyclotomic classes of order six and eight.

Cryptography and Security