Optimum distance flag codes from spreads via perfect matchings in graphs
| Autor: | Xaro Soler-Escrivà, Miguel Ángel Navarro-Pérez, Clementa Alonso-González |
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| Přispěvatelé: | Universidad de Alicante. Departamento de Matemáticas, Grupo de Álgebra y Geometría (GAG), Ministerio de Ciencia e Innovación (España) |
| Rok vydání: | 2021 |
| Předmět: |
FOS: Computer and information sciences
Matemáticas Computer Science - Information Theory Type (model theory) Combinatorics Set (abstract data type) Cardinality Network coding Álgebra FOS: Mathematics Discrete Mathematics and Combinatorics Mathematics - Combinatorics Perfect matching Spreads Prime power Mathematics Subspace codes Algebra and Number Theory Information Theory (cs.IT) Finite field Geometría y Topología Combinatorics (math.CO) Focus (optics) Graphs Flag codes Vector space Flag (geometry) |
| Zdroj: | RUA. Repositorio Institucional de la Universidad de Alicante Universidad de Alicante (UA) |
| Popis: | In this paper, we study flag codes on the vector space $${{\mathbb {F}}}_q^n$$ F q n , being q a prime power and $${{\mathbb {F}}}_q$$ F q the finite field of q elements. More precisely, we focus on flag codes that attain the maximum possible distance (optimum distance flag codes) and can be obtained from a spread of $${{\mathbb {F}}}_q^n$$ F q n . We characterize the set of admissible type vectors for this family of flag codes and also provide a construction of them based on well-known results about perfect matchings in graphs. This construction attains both the maximum distance for its type vector and the largest possible cardinality for that distance. |
| Databáze: | OpenAIRE |
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