On two-fold packings of radius-1 balls in Hamming graphs

A λ-fold r-packing in a Hamming metric space is a code C such that the radius-r balls centered in C cover each vertex of the space by not more than λ-times. The well-known r- error-correcting codes correspond to the case λ = 1. We propose asymptotic bounds for q-ary 2-fold 1-packings as q grows, find that the maximum size of a binary 2-fold 1-packing of length 9 is 96, and derive upper bounds for the size of a binary λ-fold 1 -packing.