Title :
The packing radius of a code and partitioning problems: The case for poset metrics
Author :
D´Oliveira, Rafael Gregorio Lucas ; Firer, M.
Author_Institution :
State Univ. of Campinas, Campinas, Brazil
fDate :
June 29 2014-July 4 2014
Abstract :
Considering a poset metric as a generalization of Hamming´s metric, the packing radius of a code is not necessarily a function of the minimal distance. In this work we show, without any restriction on the poset, that the relation between the weight and the packing radius of a vector is equivalent to a generalization of the classical partition problem. We also generalize the well renown heuristic and deterministic algorithms of Karmakar-Karp and Korf, respectively, using an algebraic approach to the Differencing Method.
Keywords :
Hamming codes; encoding; Hamming metric; classical partition problem; deterministic algorithms; differencing method; heuristic algorithms; packing radius; partitioning problems; poset metrics case; Linear codes; Matrices; Measurement; Partitioning algorithms; Vectors;
Conference_Titel :
Information Theory (ISIT), 2014 IEEE International Symposium on
Conference_Location :
Honolulu, HI
DOI :
10.1109/ISIT.2014.6875375