Neil Sloane showed that the problem of determine the maximum size of a binary
code of constant weight 2 that can correct a single adjacent transposition is
equivalent to finding the packing number of a certain graph. In this paper we
solve this open problem by finding the packing number of the double vertex
graph (2-token graph) of a path graph. This double vertex graph is isomorphic
to the Sloane's graph. Our solution implies a conjecture of Rob Pratt about the
ordinary generating function of sequence A085680.Comment: 21 pages, 7 figures. V2: 22 pages, more figures added. V3. minor
corrections based on referee's comments. One figure corrected. The title "On
an error correcting code problem" has been change
