| Full text | |
| Author(s): |
Miyamoto, Gabriella Akemi
;
Firer, Marcelo
Total Authors: 2
|
| Document type: | Journal article |
| Source: | IEEE TRANSACTIONS ON INFORMATION THEORY; v. 66, n. 10, p. 12-pg., 2020-10-01. |
| Abstract | |
A tiling of F-2(n) (considered as a graph) gives rise to a perfect code (according to a given metric) if the basic tile is a metric ball. We are concerned with metrics on F-2(n) that are determined by a weight which respects the support of vectors (TS-metrics) and in this case, a perfect code is called TS-perfect. We consider all the tilings of F-2(n) by tiles with up to 8 elements (which are classified in the literature) and determine which of them give rise to a TS-perfect code. In the sequence, for those tilings that give rise to a perfect code for some TS-metric, we classify the TS-metrics (up to equivalence) that turn it into a perfect code. Also, we give a general construction to obtain TS-perfect codes out of given TS-perfect codes, by proving that concatenation of two TS-perfect codes is by itself a TS-perfect code. (AU) | |
| FAPESP's process: | 13/25977-7 - Security and reliability of Information: theory and practice |
| Grantee: | Marcelo Firer |
| Support Opportunities: | Research Projects - Thematic Grants |