Optimal Anticodes, Diameter Perfect Codes, Chains and Weights
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Let P be a poset on [n] = {1,2,...,n}, F^n_q 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 F^n_q which are induced by chain orders P over [n] and weights w over F_q. Such family of metrics extend the Niederreiter-Rosenbloom- Tsfasman metrics (when the weight is the Hamming weight). We determine the cardinality and completely classify all optimal anticodes and determine all diameter perfect codes for some instances on these spaces.
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