Zobrazeno 1 - 7
of 7
pro vyhledávání: '"Jesús Carrillo-Pacheco"'
Autor:
Jesús Carrillo-Pacheco
Publikováno v:
Mathematics, Vol 12, Iss 6, p 858 (2024)
The Plücker matrix BL(n,E) of the Lagrangian Grassmannian L(n,E), is determined by the linear envelope ⟨L(n,E)⟩ of the Lagrangian Grassmannian. The linear envelope ⟨L(n,E)⟩ is the intersection of linear relations of Plücker of Lagrangian Gr
Externí odkaz:
https://doaj.org/article/5a2c0c1f8aec4e1bb5ecc3b5926851e5
Publikováno v:
Boletín de la Sociedad Matemática Mexicana. 27
We show that for every linear section of a Grassmannian over a finite field $${{\mathbb {F}}}_q$$ , in addition to the evaluation code associated to the $${{\mathbb {F}}}_q$$ -rational points of the section, there exists a parity check code. Instance
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9c6ebac7d9c21637d1547e12a29707ba
https://doi.org/10.1007/s40590-021-00351-1
https://doi.org/10.1007/s40590-021-00351-1
Publikováno v:
Boletín de la Sociedad Matemática Mexicana. 25:747-758
We obtain descriptions of the Lagrangian–Grassmannian code (Carrillo-Pacheco and Zaldivar in Des Codes Cryptogr 60:291–268, 2011) as a linear code associated with an FFN(1, q)-projective variety (Carrillo-Pacheco and Zaldivar in Adv Math Commun 1
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::00bed443e6cf472ebad5055893135b8c
https://doi.org/10.1007/s40590-018-0219-5
https://doi.org/10.1007/s40590-018-0219-5
Publikováno v:
Special Matrices, Vol 6, Iss 1, Pp 237-248 (2018)
The aim of this paper is twofold. First, we show a connection between the Lagrangian- Grassmannian variety geometry defined over a finite field with q elements and the q-ary Low-Density Parity- Check codes. Second, considering the Lagrangian-Grassman
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bf38578c4a87916f75b3326a20c5673d
https://doaj.org/article/5ddf4715a14d4f5386438784deebec5a
https://doaj.org/article/5ddf4715a14d4f5386438784deebec5a
Publikováno v:
Advances in Mathematics of Communications. 10:209-220
For projective varieties defined over a finite field ${\mathbb F}_q$ we show that they contain a unique subvariety that satisfies the Finite Field Nullstellensatz property [1,2], for homogeneous linear polynomials over ${\mathbb F}_q$. Using these su
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::edab4c57174118af14f78ad7f5b5b9cf
https://doi.org/10.3934/amc.2016001
https://doi.org/10.3934/amc.2016001
Publikováno v:
Designs, Codes and Cryptography. 60:291-298
Using the Lagrangian---Grassmannian, a smooth algebraic variety of dimension n(n + 1)/2 that parametrizes isotropic subspaces of dimension n in a symplectic vector space of dimension 2n, we construct a new class of linear codes generated by this vari
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::78370ae3dc4ce6fe4393124a52daf784
https://doi.org/10.1007/s10623-010-9434-4
https://doi.org/10.1007/s10623-010-9434-4
Publikováno v:
Lecture Notes in Computer Science ISBN: 9783319186801
C2SI
C2SI
Using Plucker coordinates we construct a matrix whose columns parametrize all projective isotropic lines in a symplectic space E of dimension 4 over a finite field \(\mathbb{F}_{q}\). As an application of this construction we explicitly obtain the sm
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e0e2094ec85bb8a36722f46a5aaa0622
https://doi.org/10.1007/978-3-319-18681-8_19
https://doi.org/10.1007/978-3-319-18681-8_19
