On the Nonexistence of the Ding-Helleseth-Martinsens Constructions of Almost Difference Set for Cyclotomic Classes of Order 6
This resolves a specific theoretical gap in sequence design for communication systems, but it is incremental as it extends prior work to a new order.
The paper tackled the problem of constructing pseudorandom sequences with optimal three-level autocorrelation for CDMA systems by investigating the Ding-Helleseth-Martinsens Constructions for cyclotomic classes of order 6, and it proved that no such constructions exist.
Pseudorandom sequences with optimal three-level autocorrelation have important applications in CDMA communication systems. Constructing the sequences with three-level autocorrelation is equivalent to finding cyclic almost difference sets as their supports. In a paper of Ding, Helleseth, and Martinsen, the authors developed a new method known as the Ding-Helleseth-Martinsens Constructions in literature to construct the almost difference set using product set between GF(2) and union sets of cyclotomic classes of order 4. In this correspondence, we show that there do not exist such constructions for cyclotomic classes of order 6.