2012/10/28 by Yuichiro Fujiwara, Fujiwara, Yuichiro
Computer Science · Engineering · Mathematics · #05B05 (Primary) 05E18 #94B25 (Secondary) #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems #math.CO #msc:05B05 #msc:05E18 #msc:94B25
paper · pdf · doi:10.48550/arxiv.1210.7516
12 pages, no figures
arxiv created 2012/10/28 · openalex publication_date 2012/10/28 · arxiv updated 2012/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Steiner 2-design of block size k is an ordered pair (V, B) of finite sets such that B is a family of k-subsets of V in which each pair of elements of V appears exactly once. A Steiner 2-design is said to be r-even-free if for every positive integer i =< r it contains no set of i elements of B in which each element of V appears exactly even times. We study the even-freeness of a Steiner 2-design when the cyclic group acts regularly on V. We prove the existence of infinitely many nontrivial Steiner 2-designs of large block size which have the cyclic automorphisms and higher even-freeness than the trivial lower bound but are not the points and lines of projective geometry.