An orbital construction of optimum distance flag codes
| Autor: | Clementa Alonso-González, Miguel Ángel Navarro-Pérez, Xaro Soler-Escrivà |
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| Přispěvatelé: | Ministerio de Ciencia e Innovación (España), Universidad de Alicante. Departamento de Matemáticas, Grupo de Álgebra y Geometría (GAG) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
FOS: Computer and information sciences
Matemáticas Computer Science - Information Theory General linear group Field (mathematics) 0102 computer and information sciences 01 natural sciences Theoretical Computer Science Combinatorics Dimension (vector space) Network coding Álgebra 0101 mathematics Spreads Prime power Mathematics Subspace codes Algebra and Number Theory Information Theory (cs.IT) Applied Mathematics 010102 general mathematics General Engineering Orbit codes Linear subspace Finite field 010201 computation theory & mathematics Geometría y Topología Flag codes Vector space Flag (geometry) |
| Zdroj: | RUA. Repositorio Institucional de la Universidad de Alicante Universidad de Alicante (UA) |
| Popis: | Flag codes are multishot network codes consisting of sequences of nested subspaces (flags) of a vector space Fnq , where q is a prime power and Fq, the finite field of size q. In this paper we study the construction on F2kq of full flag codes having maximum distance (optimum distance full flag codes) that can be endowed with an orbital structure provided by the action of a subgroup of the general linear group. More precisely, starting from a subspace code of dimension k and maximum distance with a given orbital description, we provide sufficient conditions to get an optimum distance full flag code on F2kq having an orbital structure directly induced by the previous one. In particular, we exhibit a specific orbital construction with the best possible size from an orbital construction of a planar spread on F2kq that strongly depends on the characteristic of the field. The authors receive financial support from Ministerio de Ciencia e Innovación (PID2019-108668GB-I00). The second author is supported by Generalitat Valenciana and Fondo Social Europeo (ACIF/2018/196). |
| Databáze: | OpenAIRE |
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