Constructions of Low Rank Relative Difference Sets in 2-Groups Using Galois Rings

✍ Scribed by Qing Xiang; James A. Davis

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 167 KB
• Volume: 6
• Category: Article
• ISSN: 1071-5797
• DOI: 10.1006/ffta.1999.0275

✦ Synopsis

In this paper, we "rst determine the exact values of s(2, t), a function de"ned by X.-D. Hou [preprint], which depends on the structure of GR(4, t). This result gives the exact range of parameters of the partial di!erence sets in 9R constructed by Chen et al. (J. Combin. ¹heory Ser. A 76 (1996), 179}196) and Hou (preprint). Second, we construct a new family of (2R, 2R, 2R, 2R) relative di!erence sets in abelian 2-groups of rank as low as t#U R V. This is a signi"cant reduction over the previous minimum of 2t found in Davis (Discrete Math. 103 (1992), 7}15).