Optimal Anticodes, Diameter Perfect Codes, Chains and Weights

Let {P} be a partial order on [{n}] = \{1,2,\ldots,{n}\} , \mathbb {F}_{q}^{n} be the linear space of {n} -tuples over a finite field \mathbb {F}_{q} and {w} be a weight on \mathbb {F}_{q} . In this paper, we consider metrics on \mathbb {F}_{q}^{n} induced by chain orders {P} over [{n}] and weights {w} over \mathbb {F}_{q} , and we determine the cardinality of all optimal anticodes and completely classify them. Moreover, we determine all diameter perfect codes for a set of relevant instances on the aforementioned metric spaces.