Codes with a poset metric

Niederreiter generalized the following classical problem of coding theory: given a finite field F-4 and integers n > k greater than or equal to 1, find the largest minimum distance achievable by a linear code over F-q, of length n and dimension k. In this paper we place this problem in the more general setting of a partially ordered set and define what we call poset-codes. In this context, Niederreiter's setting may be viewed as the disjoint union of chains. We extend some of Niederreiter's bounds and also obtain bounds for posets which are the product of two chains.