Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 546015, 4 pages
doi:10.1155/2010/546015
Research Article

Alon-Babai-Suzuki's Conjecture Related to Binary Codes in Nonmodular Version

K.-W. Hwang,1 T. Kim,2 L. C. Jang,3 P. Kim,4 and Gyoyong Sohn5

1Department of Mathematics, Donga-A University, Pusan 604-714, South Korea
2Division of General Edu.-Math., Kwangwoon University, Seoul 139-701, South Korea
3Department of Mathematics and Computer Science, Konkook University, Chungju 139-701, South Korea
4Department of Mathematics, Kyungpook National University, Taegu 702-701, South Korea
5Department of Computer Science, Chungbuk National University, Cheongju 361-763, South Korea

Received 23 August 2009; Accepted 22 January 2010

Academic Editor: Ram N. Mohapatra

Copyright © 2010 K.-W. Hwang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let K={k1,k2,…,kr} and L={l1,l2,…,ls} be sets of nonnegative integers. Let ℱ={F1,F2,…,Fm} be a family of subsets of [n] with [Fi]∈K for each i and |Fi∩Fj|∈L for any i≠j. Every subset Fe of [n] can be represented by a binary code a=(a1,a2,…,an) such that ai=1 if i∈Fe and ai=0 if i∉Fe. Alon et al. made a conjecture in 1991 in modular version. We prove Alon-Babai-Sukuki's Conjecture in nonmodular version. For any K and L with n≥s+max⁡ki, |F|≤(n-1s)+(n-1s-1)+⋯+(n-1s-2r+1).