TY - JOUR
T1 - Alon-babai-suzuki's conjecture related to binary codes in nonmodular version
AU - Hwang, K. W.
AU - Kim, T.
AU - Jang, L. C.
AU - Kim, P.
AU - Sohn, Gyoyong
PY - 2010
Y1 - 2010
N2 - Let K={ k1, k2,⋯, kr} and L={ l1, l2,⋯, ls} be sets of nonnegative integers. LetF={ F1, F2,⋯, Fm} be a family of subsets of [ n ] with [ Fi]∈K for each i and | F iF∩j|∈L for any iεj. Every subset F eof [ n ] can be represented by a binary code a =(a1, a2,⋯, an) such that a i =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-1 s)+(n-1 s-1)+⋯+(n-1 s-2r+1).
AB - Let K={ k1, k2,⋯, kr} and L={ l1, l2,⋯, ls} be sets of nonnegative integers. LetF={ F1, F2,⋯, Fm} be a family of subsets of [ n ] with [ Fi]∈K for each i and | F iF∩j|∈L for any iεj. Every subset F eof [ n ] can be represented by a binary code a =(a1, a2,⋯, an) such that a i =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-1 s)+(n-1 s-1)+⋯+(n-1 s-2r+1).
UR - https://www.scopus.com/pages/publications/79956135808
U2 - 10.1155/2010/546015
DO - 10.1155/2010/546015
M3 - Article
AN - SCOPUS:79956135808
SN - 1025-5834
VL - 2010
JO - Journal of Inequalities and Applications
JF - Journal of Inequalities and Applications
M1 - 546015
ER -