Abstract

By combining a lattice subgroup diagram of (Formula presented.) with a weighted poset metric, we introduce a new weighted coordinates poset metric for codes over (Formula presented.), called the (Formula presented.) -poset metric. When I is an ideal in a poset, the concept of I-perfect codes with an (Formula presented.) -poset metric is investigated. We obtain a Singleton bound for codes with the (Formula presented.) -poset metric and define MDS codes. When the poset in the poset metric is a chain, we provide sufficient conditions for a code with the (Formula presented.) -poset metric to be r-perfect for some (Formula presented.).