José Ignacio Iglesias Curto

José Ignacio Iglesias Curto
Universidad de Salamanca · Department of Mathematics

PhD in Mathematics

About

13
Publications
1,910
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56
Citations
Additional affiliations
October 2014 - present
Universidad de Salamanca
Position
  • Professor
October 2009 - September 2014
Universidad de Salamanca
Position
  • Professor

Publications

Publications (13)
Article
Convolutional Goppa codes (CGC) were defined in Appl. Algebra Eng. Comm. Comput., vol. 15, pp. 51-61, 2004 and IEEE Trans. Inf. Theory, vol. 52, 340-344, 2006. In this paper, we prove that every convolutional code is a CGC defined over a smooth curve over BBF q(z) and we give an explicit construction of convolutional codes as CGC over the projectiv...
Article
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We show that the free distance, as a function on a space parameterizing a family of convolutional codes, is a lower-semicontinuous function and that, therefore, the property of being Maximum Distance Separable (MDS) is an open condition. For a class of convolutional codes, an algorithm is offered to compute the free distance. The behaviour of the f...
Article
Full-text available
We define a new class of Convolutional Codes in terms of fibrations of algebraic varieties generalizaing our previous constructions of Convolutional Goppa Codes. Using this general construction we can give several examples of Maximum Distance Separable (MDS) Convolutional Codes. Comment: 10 pages
Article
Convolutional codes have the structure of an F[z]-module. To study their properties it is desirable to classify them as the points of a certain algebraic variety. By considering the correspondence of submodules and the points of certain quotient schemes, and the inclusion of these as subvarieties of certain Grassmannians, one has a one-to-one corre...
Article
We present the family of generalized AG convolutional codes, constructed by using algebraic geometric tools. This construction extends block generalized AG codes on the one hand and several algebraic constructions of convolutional codes on the other. The tools employed to define these codes are also used to obtain information about their parameters...
Article
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Decoding of convolutional codes poses a significant challenge for coding theory. Classical methods, based on e.g. Viterbi decoding, suffer from being computationally expensive and are restricted therefore to codes of small complexity. Based on analogies with model predictive optimal control, we propose a new iterative method for convolutional decod...
Article
Full-text available
An iterative decoding algorithm for convolutional codes is presented. It successively processes $N$ consecutive blocks of the received word in order to decode the first block. A bound is presented showing which error configurations can be corrected. The algorithm can be efficiently used on a particular class of convolutional codes, known as doubly...
Conference Paper
The algebraic geometric tools used by Goppa to construct block codes with good properties have been also used successfully in the setting of convolutional codes. We present here this construction carried out over elliptic curves, yielding a variety of codes which are optimal with respect to different bounds. We provide a number of examples for diff...
Article
Full-text available
En el artículo se definen los códigos Goppa a través de curvas algebraicas y la construccion de sus correspondientes códigos duales. In this correspondence, we define convolutional Goppa codes over algebraic curves and construct their corresponding dual codes. Examples over the projective line and over elliptic curves are described, obtaining in pa...
Article
Full-text available
In this correspondence, we define convolutional Goppa codes over algebraic curves and construct their corresponding dual codes. Examples over the projective line and over elliptic curves are described, obtaining in particular some maximum-distance separable (MDS) convolutional codes.
Article
Full-text available
Resumen Convolutional codes can be regarded as discrete time linear systems. This rela-tionship has been studied along decades, and concepts from both theories have found their counterparts into the other one. In this context, decoding of a received word can be interpreted as a tracking pro-blem. This should allow to give practical decoding algorit...

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