On the Nonexistence of the Ding-Helleseth-Martinsens Constructions of Almost Difference Set for Cyclotomic Classes of Order 6

2016/02/19 by Qi, Minglong, Xiong, Shengwu, Yuan, Jinbgling +2
#Cryptography and Security (cs.CR) #FOS: Computer and information sciences

paper · doi:10.48550/arxiv.1602.06007

Abstract

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.

Related

• On a Class of Almost Difference Sets Constructed by Using the Ding-Helleseth-Martinsens Constructions
• Almost Difference Sets from Unions of Cyclotomic Classes of Order 14
• Partial direct product difference sets and sequences with ideal autocorrelation
• A Survey on Almost Difference Sets
• Nearly perfect sequences with arbitrary out-of-phase autocorrelation