Codes with a poset metric Original Research Article

Niederreiter generalized the following classical problem of coding theory: given a finite field Fq and integers n > k ⩾ 1, find the largest minimum distance achievable by a linear code over Fq 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, Niederreiterʹs setting may be viewed as the disjoint union of chains. We extend some of Niederreiterʹs bounds and also obtain bounds for posets which are the product of two chains.