Artículos de revistas
Linear codes on posets with extension property
Registro en:
Discrete Mathematics. Elsevier Science Bv, v. 317, n. 1, n. 13, 2014.
0012-365X
1872-681X
WOS:000331159100001
10.1016/j.disc.2013.11.001
Autor
Barg, A
Felix, LV
Firer, M
Spreafico, MVP
Institución
Resumen
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) 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. We also study the question of whether these invariants are preserved under standard operations on posets such as the ordinal sum and the like. (C) 2013 Published by Elsevier B.V. 317 1 13 NSA [H98230-12-1-0260] Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) NSF [CCF0916919, CCF1217245, CCF1217894, DMS1101697] Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) NSA [H98230-12-1-0260] FAPESP [2007/56052-8, 2102/20181-7] NSF [CCF0916919, CCF1217245, CCF1217894, DMS1101697]