A theorem about linear rank inequalities that depend on the characteristic of the finite field
A linear rank inequality is a linear inequality that holds by dimensions of vector spaces over any finite field. A characteristic-dependent linear rank inequality is also a linear inequality that involves dimensions of vector spaces but this holds over finite fields of determined characteristics, an...
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| Format: | Article |
| Language: | Spanish |
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Universidad Nacional de Trujillo
2022-07-01
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| Series: | Selecciones Matemáticas |
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| Online Access: | https://revistas.unitru.edu.pe/index.php/SSMM/article/view/4177 |
| _version_ | 1817995767161290752 |
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| author | Victor Peña-Macias |
| author_facet | Victor Peña-Macias |
| author_sort | Victor Peña-Macias |
| collection | DOAJ |
| description | A linear rank inequality is a linear inequality that holds by dimensions of vector spaces over any finite field. A characteristic-dependent linear rank inequality is also a linear inequality that involves dimensions of vector spaces but this holds over finite fields of determined characteristics, and does not in general hold over other characteristics. In this paper, using as guide binary matrices whose ranks depend on the finite field where they are defined, we show a theorem which explicitly produces characteristic-dependent linear rank inequalities; this theorem generalizes results previously obtained in the literature. |
| first_indexed | 2024-04-14T02:12:34Z |
| format | Article |
| id | doaj.art-d032e380ca9e4b4b88261f45b43337f7 |
| institution | Directory Open Access Journal |
| issn | 2411-1783 |
| language | Spanish |
| last_indexed | 2024-04-14T02:12:34Z |
| publishDate | 2022-07-01 |
| publisher | Universidad Nacional de Trujillo |
| record_format | Article |
| series | Selecciones Matemáticas |
| spelling | doaj.art-d032e380ca9e4b4b88261f45b43337f72022-12-22T02:18:24ZspaUniversidad Nacional de TrujilloSelecciones Matemáticas2411-17832022-07-0190115016010.17268/sel.mat.2022.01.12A theorem about linear rank inequalities that depend on the characteristic of the finite fieldVictor Peña-Macias0https://orcid.org/0000-0002-4020-015XFacultad de Ciencias, Universidad Nacional de Colombia, Colombia.A linear rank inequality is a linear inequality that holds by dimensions of vector spaces over any finite field. A characteristic-dependent linear rank inequality is also a linear inequality that involves dimensions of vector spaces but this holds over finite fields of determined characteristics, and does not in general hold over other characteristics. In this paper, using as guide binary matrices whose ranks depend on the finite field where they are defined, we show a theorem which explicitly produces characteristic-dependent linear rank inequalities; this theorem generalizes results previously obtained in the literature.https://revistas.unitru.edu.pe/index.php/SSMM/article/view/4177mutually complementary vector spacesbinary matrixfinite fieldentropylinear rank inequality |
| spellingShingle | Victor Peña-Macias A theorem about linear rank inequalities that depend on the characteristic of the finite field Selecciones Matemáticas mutually complementary vector spaces binary matrix finite field entropy linear rank inequality |
| title | A theorem about linear rank inequalities that depend on the characteristic of the finite field |
| title_full | A theorem about linear rank inequalities that depend on the characteristic of the finite field |
| title_fullStr | A theorem about linear rank inequalities that depend on the characteristic of the finite field |
| title_full_unstemmed | A theorem about linear rank inequalities that depend on the characteristic of the finite field |
| title_short | A theorem about linear rank inequalities that depend on the characteristic of the finite field |
| title_sort | theorem about linear rank inequalities that depend on the characteristic of the finite field |
| topic | mutually complementary vector spaces binary matrix finite field entropy linear rank inequality |
| url | https://revistas.unitru.edu.pe/index.php/SSMM/article/view/4177 |
| work_keys_str_mv | AT victorpenamacias atheoremaboutlinearrankinequalitiesthatdependonthecharacteristicofthefinitefield AT victorpenamacias theoremaboutlinearrankinequalitiesthatdependonthecharacteristicofthefinitefield |