The Problem Of Maximal Separation On 2-D Arrays

This paper considers a maximal separation problem in two-dimensional digital data.In an m×n array,we consider a fixed number of elements,say l,with 2 l mn.We study the problem of separating the l elements on the m×n array such that the minimum l~1distance between any two elements is as large as possible.The maximal separation problem may be considered as an extension or simplification of the interleaving schemes for correcting cluster errors in two-dimensional digital data.We focus one particular codeword such that any two different symbols from this codeword are separated as much as possible.For general m,n and l,we derive a lower bound of the maximum distance of separation for the case of n-1<(l-1)(m-1).The maximum separation has been well-studied for the case of n-1(l-1)(m-1).We derive the result of the maximum number of elements so that the distance of separation between any two elements is at least d for the case of m=5.In addition,we derive the maximum distance of separation for the case of l=6,m 5 and we also derive an upper bound of the maximum distance separation for the case of l=7.