Alon-babai-suzuki's conjecture related to binary codes in nonmodular version

K. W. Hwang; T. Kim; L. C. Jang; P. Kim; Gyoyong Sohn

doi:10.1155/2010/546015

Alon-babai-suzuki's conjecture related to binary codes in nonmodular version

K. W. Hwang
, T. Kim
, L. C. Jang
, P. Kim
, Gyoyong Sohn

Dong-A University
Kwangwoon University
Konkuk University
Chungbuk National University

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Let K={ k₁, k₂,⋯, k_r} and L={ l₁, l₂,⋯, l_s} be sets of nonnegative integers. LetF={ F₁, F₂,⋯, F_m} be a family of subsets of [ n ] with [ F_i]∈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,⋯, a_n) such that a i =1∈if i F_e and a_i =0 if i∈ F_e. 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 k_i, | F |≥ (^n-1 _s)+(^n-1 _s-1)+⋯+(^n-1 _s-2r+1).

Original language	English
Article number	546015
Journal	Journal of Inequalities and Applications
Volume	2010
DOIs	https://doi.org/10.1155/2010/546015
State	Published - 2010

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@article{30b00877603b4477b235f06891b4857b,

title = "Alon-babai-suzuki's conjecture related to binary codes in nonmodular version",

abstract = "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).",

author = "Hwang, \{K. W.\} and T. Kim and Jang, \{L. C.\} and P. Kim and Gyoyong Sohn",

year = "2010",

doi = "10.1155/2010/546015",

language = "English",

volume = "2010",

journal = "Journal of Inequalities and Applications",

issn = "1025-5834",

publisher = "Springer Nature",

}

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 -

Alon-babai-suzuki's conjecture related to binary codes in nonmodular version

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