| Full text | |
| Author(s): |
Barg, Alexander
[1, 2, 3]
;
Felix, Luciano V.
[4, 5]
;
Firer, Marcelo
[4]
;
Spreafico, Marcos V. P.
[4, 6]
Total Authors: 4
|
| Affiliation: | [1] Univ Maryland, Dept Elect & Comp Engn, College Pk, MD 20742 - USA
[2] Univ Maryland, Syst Res Inst, College Pk, MD 20742 - USA
[3] Russian Acad Sci, Inst Problems Informat Transmiss, Moscow - Russia
[4] Univ Estadual Campinas, IMECC UNICAMP, BR-13083859 Campinas, SP - Brazil
[5] Univ Fed Rural Rio de Janeiro, ICE UFRRJ, BR-23890000 Seropedica, RJ - Brazil
[6] Univ Fed Mato Grosso do Sul, INMA UFMS, BR-79070900 Campo Grande, RS - Brazil
Total Affiliations: 6
|
| Document type: | Journal article |
| Source: | DISCRETE MATHEMATICS; v. 317, p. 1-13, FEB 28 2014. |
| Web of Science Citations: | 5 |
| Abstract | |
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. (AU) | |