Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9514553 | Electronic Notes in Discrete Mathematics | 2005 | 5 Pages |
Abstract
Let G=Ãi=1nCâi be the direct product of cycles. It is proved that for any râ¥1, and any nâ¥2, each connected component of G contains an r-perfect code provided that each âi is a multiple of rn+(r+1)n. On the other hand, if a code of G contains a given vertex and its canonical local vertices, then any âi is a multiple of rn+(r+1)n. It is also proved that an r-perfect code (râ¥2) of G is uniquely determined by n vertices and it is conjectured that for râ¥2 no other codes in G exist than the constructed ones.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Simon Å pacapan,