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

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).

Abstract licence: CC BY-NC-ND

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