Distance-Regular Graphs

Introduction to finite fields and their applications: Factorization of Polynomials

In this paper, we consider metrics determined by hierarchical posets and give explicit formulas for the main parameters of a linear code: the minimum distance and the packing, covering, and Chebyshev radii of a code. We also present ten characterizations of hierarchical poset metrics, including new characterizations and simple new proofs to the known ones.

Characterization of Metrics Induced by Hierarchical Posets

In this paper we consider metrics determined by hierarchical posets and give explicit formulae for the main parameters of a linear code: the minimum distance and the packing, covering and Chebyshev radii of a code. We also present ten characterizations of hierarchical poset metrics, including new characterizations and simple new proofs to the known ones.

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Characterization of metrics induced by hierarchical posets

MacWilliams type identities for linear codes on certain pomsets: Chain, direct and ordinal sum of pomsets

It is known that being hierarchical is a necessary and suffi- cient condition for a poset to admit MacWilliams identity. In this paper, we completely characterize the structures of posets which have an associ- ation scheme structure whose relations are indexed by the poset distance between the points in the space. We also derive an explicit formula for the eigenmatrices of association schemes induced by such posets. By using the result of Delsarte which generalizes the MacWilliams identity for linear codes, we give a new proof of the MacWilliams identity for hierarchical linear poset codes.

/pdf/poset-metrics-admitting-association-schemes-and-a-new-proof-8pc7uasxw6.pdf

Dong Yeol Oh

Papers

Poset metrics admitting association schemes and a new proof of macwilliams identity