Set systems with k-wise L-intersections and codes with restricted Hamming distances. (November 2016)

• Record Type: Journal Article
• Authors: Liu, Jiuqiang; Zhang, Shenggui; Li, Shuchao; Zhang, Huihui
• Is Part Of: European journal of combinatorics. Volume 58(2016:Nov.)
• Page Start: 166
• Page End: 180
• Publication Date: 2016-11
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2016.05.006
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: In this paper, we first give a corollary to Snevily's Theorem on L -intersecting families, which implies a result that cuts by almost half the bound given by Grolmusz and Sudakov (2002), and provide a k -wise extension to the theorem by Babai et al. (2001) on set systems with L -intersections modulo prime powers which implies polynomial bounds for such families. We then extend Alon–Babai–Suzuki type inequalities on set systems to k -wise L -intersecting families and derive a result which improves the existing bound substantially for the non-modular case. We also provide the first known polynomial bounds for codes with restricted Hamming distances for all prime powers moduli p t, in contrast with Grolmusz's result from Grolmusz (2006) that for non-prime power composite moduli, no polynomial bound exists for such codes.