| Full text | |
| Author(s): |
Machado, Roberto
;
Firer, Marcelo
;
IEEE
Total Authors: 3
|
| Document type: | Journal article |
| Source: | 2019 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT); v. N/A, p. 5-pg., 2019-01-01. |
| Abstract | |
In this work we explore a family of metrics over a finite field F-q which respect the support of vectors. We show how these metrics can be obtained from the edge-weighted Hamming cube and, based on this representation we give a description of the group of linear isometries (for q > 2). Next we introduce the concept of conditional sum of metrics and determine what are the conditions that, out of two metrics respecting the support, gives rise to a new such metric. Finally we introduce the labeled-poset block metrics, a new family of metrics which respects support of vectors, filling a gap existing in the known universe of such metrics. For this family we give a full description of the group of linear isometries and determine sufficient conditions for the existence of a MacWilliams' identity. (AU) | |
| FAPESP's process: | 15/11286-8 - Metrics that agree on the support of vectors and nearest neighbor decoding |
| Grantee: | Roberto Assis Machado |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 13/25977-7 - Security and reliability of Information: theory and practice |
| Grantee: | Marcelo Firer |
| Support Opportunities: | Research Projects - Thematic Grants |