A new type of coding problem

• DOI: 10.1556/sscmath.38.2001.1-4.9
• Publication Date: 2005-10-21T19:24:10Z
• Authors: G. Brightwell; Gyula Katona
• Keywords: QA Mathematics / matematika; 0102 computer and information sciences; 01 natural sciences

Let X be an n-element finite set, and 0 Let X be an n-element finite set, and are pairs of disjoint k-element subsets of X (that is, {A1 = B1} = {A2 = B2} = k, A1 \ B1 = A2 \ B2 = Define the distance between these pairs by d(f A1;B1 g; f A2; B2 g)=min fj A1 - A2 j + B1 - B2 j; j A1 - B2 j + j B1 - A2 jg . Itisknown ([2]) that the family of all k-element subsets of X can be paired (with one exception if their number is odd) in such a way that the distance between any two pairs is at least k. Here we answer questions arising for distances larger than k.