Perfect Codes for Uniform Chains Poset Metrics
  The class of poset metrics is very large and contains some interesting families of metrics. A family of metrics, based on posets which are formed from disjoint chains which have the same size, is examined. A necessary and sufficient condition, for the existence of perfect single-error-correcting codes for such poset metrics, is proved. 
Tuvi Etzion
cs.IT math.CO math.IT