Translation association schemes, poset metrics, and the shape enumerator of codes

Poset metrics form a generalization of the Hamming metric on the space Fⁿ_q. Orbits of the group of linear isometries of the space give rise to a translation association scheme. The structure of the dual scheme is important in studying duality of linear codes; this study is facilitated if the scheme is self-dual. We study the relation between self-duality of the scheme and that of the poset. We also give new examples of poset metric spaces and describe the association schemes that arise from linear isometries.