Gupta, Somi (2024) Maximum rank distance codes and partitions of affine vector spaces. [Tesi di dottorato]
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| Tipologia del documento: | Tesi di dottorato |
|---|---|
| Lingua: | English |
| Titolo: | Maximum rank distance codes and partitions of affine vector spaces |
| Autori: | Autore Email Gupta, Somi somi.gupta@unina.it |
| Data: | 11 Dicembre 2024 |
| Numero di pagine: | 92 |
| Istituzione: | Università degli Studi di Napoli Federico II |
| Dipartimento: | Matematica e Applicazioni "Renato Caccioppoli" |
| Dottorato: | Matematica e Applicazioni |
| Ciclo di dottorato: | 37 |
| Coordinatore del Corso di dottorato: | nome email Moscariello, Gioconda gmoscari@unina.it |
| Tutor: | nome email Trombetti, Rocco [non definito] |
| Data: | 11 Dicembre 2024 |
| Numero di pagine: | 92 |
| Parole chiave: | linear set, linearized polynomial, finite field, finite projective space, subgeometry, rank metric codes |
| Settori scientifico-disciplinari del MIUR: | Area 01 - Scienze matematiche e informatiche > MAT/03 - Geometria |
| Depositato il: | 29 Ott 2025 09:16 |
| Ultima modifica: | 12 Ago 2026 05:37 |
| URI: | https://www.fedoa.unina.it/id/eprint/16433 |
Abstract
This thesis summarises the work carried out during the three years of my PhD under the scientific supervision of Prof. Rocco Trombetti. In this thesis, we explored some aspects where coding theory and geometry feed off each other, with results and techniques one informing the other. We especially see the link between MRD codes with large minimum distances (hence better error correction capabilities) with linear sets and vector space partitions. We dig deeper into their geometric descriptions. This thesis contains three chapters. The first chapter is an introductory work, providing all the necessary background and foundational concepts to understand the thesis. Chapter 2 describes the connection between linear sets and MRD codes. Chapter 3 focuses on affine vector space partitions, establishing a connection between the spreads of affine spaces and the spreads of quadrics.
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