Optimal Anticodes, Diameter Perfect Codes, Chains and Weights

Let P be a partial order on [n] = {1,2,...,n}, F
_q
ⁿ
be the linear space of n-tuples over a finite field F
_q
and w be a weight on 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.