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

作者：Hwang K W^*; Kim T; Jang L C; Kim P; Sohn Gyoyong

来源：Journal of Inequalities and Applications, 2010, 546015.

DOI：10.1155/2010/546015

Let K = {k(1), k(2),..., k(r)} and L = {l(1), l(2),..., l(s)} be sets of nonnegative integers. Let F = {F(1), F(2),..., F(m)} be a family of subsets of [n] with [F(i)] is an element of K for each i and vertical bar F(i) boolean AND F(j)vertical bar is an element of L for any i not equal j. Every subset F(e) of [n] can be represented by a binary code a = (a(1), a(2),..., a(n)) such that a(i) = 1 if i is an element of F(e) and a(i) = 0 if i is not an element of 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), vertical bar F vertical bar <= (n-1 s) + (n-1 s-1) + ... + (n-1 s-2r+1).

• 出版日期2010