Tuyển tập các báo cáo nghiên cứu khoa học về toán học trên tạp chí toán học quốc tế đề tài: New infinite families of 3-designs from algebraic curves of higher genus over finite fields. | New infinite families of 3-designs from algebraic curves of higher genus over finite fields Byeong-Kweon Oh Hoseog Yu y Department of Applied Mathematics Department of Applied Mathematics Sejong University Seoul 143-747 Korea Sejong University Seoul 143-747 Korea bkoh@ hsyu@ Submitted Mar 7 2007 Accepted Oct 26 2007 Published Nov 5 2007 Mathematics Subject Classification 05B05 Abstract In this paper we give a simple method for computing the stabilizer subgroup of D f a 2 Fq I there is a p 2 Fq such that fin f a in PSL2 Fq where q is a large odd prime power n is a positive integer dividing q 1 greater than 1 and f x 2 Fq x . As an application we construct new infinite families of 3-designs. 1 Introduction A t v k A design is a pair X B where X is a v-element set of points and B is a collection of k-element subsets of X called blocks such that every t-element subset of X is contained in precisely A blocks. For general facts and recent results on t-designs see 1 . There are several ways to construct family of 3-designs one of them is to use codewords of some particular codes over Z4. For example see 5 6 10 and 11 . For the list of known families of 3-designs see 8 . Let Fq be a finite field with odd characteristic and e Fq U 1 where 1 is a symbol. Let G PGL2 Fq be a group of linear fractional transformations. Then it is well known that the action PGL2 Fq X e e is triply transitive. Therefore for any subset X c e we have a 3 q 1 XI J X 6 GX3 design where GX is the setwise stabilizer of X 3 in G see 1 Proposition in . In general it is very difficult to calculate the order of the stabilizer GX. Recently Cameron Omidi and Tayfeh-Rezaie computed all possible This author s work was supported by the Korean Research Foundation Grant funded by the Korean Government MOEHRD KRF-2005-070-C00004 . y Correspondence author THE ELECTRONIC JOURNAL OF COMBINATORICS 14 2007 N25 1 A such that there exists a 3 q 1 k A design admitting PGL2 Fq or PSL2 Fq .
