Edgar Martinez-Moro
Universidad de Valladolid, Mathematics, Faculty Member
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We show the combinatorial structure of Z² modulo sublattices similar to Z². The tool we use for dealing with this purpose is the notion of association scheme. We classify when the scheme defined by the lattice is imprimitive and... more
We show the combinatorial structure of Z² modulo sublattices similar to Z². The tool we use for dealing with this purpose is the notion of association scheme. We classify when the scheme defined by the lattice is imprimitive and characterize its decomposition in terms of the decomposition of the Gaussian integer defining the lattice. This arises in the classification of different forms of tiling Z² by lattices of this type. The main application of these structures is that they are closely related to two-dimensional signal constellations with a Mannheim metric in the coding theory.
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Page 1. Ciclos, ideales y códigos binarios Borges-Quintana, M.(a)*;Borges-Trenard, MA(a); Fitzpatrick, P.(b); Martınez-Moro, E.(c)** (a) Dpto. de Matemática, FCMC, Universidad de Oriente, Santiago de Cuba, Cuba. mijail@mbq ...
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A Private Information Retrieval (PIR) scheme allows users to retrieve data from a database without disclosing to the server information about the identity of the data retrieved. A coded storage in a distributed storage system with... more
A Private Information Retrieval (PIR) scheme allows users to retrieve data from a database without disclosing to the server information about the identity of the data retrieved. A coded storage in a distributed storage system with colluding servers is considered in this work, namely the approach in [1] which considers an storage and retrieval code with a transitive group and provides binary PIR schemes with the highest possible rate. Reed-Muller codes were considered in [1], cyclic codes are considered in this work since they have a transitive group and can be defined over a binary field as well. We show that binary PIR schemes provide a larger constellation of PIR parameters and they outperform the ones coming from Reed-Muller codes in some cases.
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Acceso de usuarios registrados. Acceso de usuarios registrados Usuario Contraseña. ...
Información del artículo Una revisión de las premisas en esquemas visuales para compartir secretos.
In this paper we introduce a binomial ideal derived from a binary linear code. We present some applications of a Gr\"obner basis of this ideal with respect to a total degree ordering. In the first application we give a decoding... more
In this paper we introduce a binomial ideal derived from a binary linear code. We present some applications of a Gr\"obner basis of this ideal with respect to a total degree ordering. In the first application we give a decoding method for the code. By associating the code with the set of cycles in a graph, we can solve the
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Page 1. PLEMATH SYSTEM: Linear and Integer Linear Programming in Mathematica System Mijail Borges-Quintana, Miguel A. Borges-Trenard Department of Mathematics. Faculty of Sciences. University of Oriente. Santiago ...
Se realiza en la E.T.S. de Arquitectura de la Universidad de Valladolid, para la titulación que se imparten en este Centro. El equipo está formado por seis profesores. Objetivos: utilizar nuevas tecnologías para estudiar las relaciones de... more
Se realiza en la E.T.S. de Arquitectura de la Universidad de Valladolid, para la titulación que se imparten en este Centro. El equipo está formado por seis profesores. Objetivos: utilizar nuevas tecnologías para estudiar las relaciones de las Matemáticas con el proyecto arquitectónico y urbano. Fomentar e incentivar el trabajo en grupo tanto por parte de los alumnos como por parte del equipo investigador. Elaborar unidades temáticas y prácticas de matemáticas, analizando construcciones arquitectónicas, prestando especial atención al Patrimonio de la Comunidad de Castilla y León. Realizar propuestas arquitectónicas nuevas, estudiando sus posibilidades geométricas. Sistemas de trabajo llevado a cabo: selección de programas informáticos adecuados a los problemas propuestos. Recopilación de material gráfico, planos, bocetos, fotografías, etc. Planteamiento y resolución clara y precisa de los temas planteados. Pensamos que el método ha favorecido el aprendizaje de los alumnos y su trabaj...
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Codes over rings is still an emerging area in coding theory. Most of the work done so far has been done on alphabets that are chain rings. As the next logical step in the development of codes over rings, some studies have been done on... more
Codes over rings is still an emerging area in coding theory. Most of the work done so far has been done on alphabets that are chain rings. As the next logical step in the development of codes over rings, some studies have been done on codes over local Frobenius rings that are not chain rings. In this work, the smallest local Frobenius rings are shown to be of order 16 and a complete list of these seven rings is given. Along the way, all local rings of order 16 are found. In addition to these rings, some commonalities, pertaining to codes, between the local Frobenius non-chain rings are shown.