Name
Abstract | ||
|---|---|---|
The labeling of the Hamming Space (Z22,dh) by the rotation group Z4 and its coordinate-wise extension to Z22n give rise to the concept of Z4-linearity. Attempts to extend this concept have been done in different ways. We deal with a natural extension question: Is there any pattern of a cyclic group G labeling of Z2n, with the Hamming or Lee metric? The answer is no. Actually, we show here that Lee spaces do not allow even labelings by abelian groups, what lead us to construct labelings by semi-direct products of abelian groups. Labelings of general Hamming spaces and of Reed-Muller codes RM(1,m) are characterized here in the context of isometry groups. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1016/S0012-365X(02)00454-5 | Discrete Mathematics |
Keywords | Field | DocType |
abelian group,coordinate-wise extension,rotation group,reed–muller codes,cyclic group,z 4 -linearity,isometry group,labelings,natural extension question,reed-muller code,hamming space,lee spaces,graphs,lee space,general hamming space,reed muller code,reed muller codes,direct product | Hamming code,Discrete mathematics,Abelian group,Combinatorics,Cyclic group,Isometry,Hamming distance,Linear code,Hamming space,Mathematics,Hamming graph | Journal |
Volume | Issue | ISSN |
260 | 1-3 | Discrete Mathematics |
Citations | PageRank | References |
1 | 0.67 | 7 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Marcelo Muniz | 1 | 1 | 1.01 |
| Sueli I. R. Costa | 2 | 21 | 8.66 |