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| Author(s): |
Roberto Assis Machado
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
| Defense date: | 2019-09-09 |
| Examining board members: |
Marcelo Firer;
Alexander Barg;
Patrick Solé;
Marcelo Muniz Silva Alves;
Carlile Campos Lavor
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| Advisor: | Marcelo Firer |
| Abstract | |
This thesis studies metrics determined by weight that are compatible with support of vectors (TS-metrics) in the context of coding theory. Its main concern, considering specific families of metrics, is to explore and understand some ''structural'' results of the metrics, namely: to describe the group of linear isometries and to establish conditions for the validity of the MacWilliams Identity (a relation between the weight distribution of a code and the weight distribution - possibly of a modified weight - of the dual code) and the MacWilliams extension property (when linear isometries between linear codes can be extended to linear isometries on the whole space).These results are first explored for the family of Gabidulin¿s comibinatorial metrics and for a new family of such metrics, the labeled-poset-block metrics. In addition, it is introduce a systematic approach to the space of all TS-metrics, first by labeling the edges of the Hamming cube. Then, we introduce a conditional operator on TS-metrics, which allows to show that any TS-metrics can be obtained, by a sequence of conditional sums of poset or combinatorial metrics. Besides this systematic study of TS-metrics, we present some relevant results concerning representation of digraphs (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 |