Artículos de revistas
Linear Codes On Posets With Extension Property
Registro en:
Discrete Mathematics. , v. 317, n. 1, p. 1 - 13, 2014.
0012365X
10.1016/j.disc.2013.11.001
2-s2.0-84888341817
Autor
Barg A.
Felix L.V.
Firer M.
Spreafico M.V.P.
Institución
Resumen
We investigate linear and additive codes in partially ordered Hamming-like spaces that satisfy the extension property, meaning that automorphisms of ideals extend to automorphisms of the poset. The codes are naturally described in terms of translation association schemes that originate from the groups of linear isometries of the space. We address questions of duality and invariants of codes, establishing a connection between the dual association scheme and the scheme defined on the dual poset (they are isomorphic if and only if the poset is self-dual). We further discuss invariants that play the role of weight enumerators of codes in the poset case. In the case of regular rooted trees such invariants are linked to the classical problem of tree isomorphism. 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