Ramamonjy ANDRIAMIFIDISOA - Academia.edu (original) (raw)
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Papers by Ramamonjy ANDRIAMIFIDISOA
Journal of Algebra and Related Topics, Dec 1, 2017
arXiv (Cornell University), Mar 19, 2012
In this paper, we use a duality between the vector space of the multi-indexed sequences over a fi... more In this paper, we use a duality between the vector space of the multi-indexed sequences over a field and the vector subspace of the sequences with finite support over this field to characterize the closed subpaces of multi-indexed sequences. Then we prove that the polynomial operator in the shift which Oberst and Willems have introduced to define time invariant discrete linear dynamical systems is the adjoint of the polynomial multiplication. We end this paper by describing these systems.
British Journal of Mathematics & Computer Science, 2016
British Journal of Mathematics & Computer Science, 2015
The vector space of the multi-indexed sequences over a field and the vector space of the sequence... more The vector space of the multi-indexed sequences over a field and the vector space of the sequences with finite support are dual to each other, with respect to an appropriate scalar product. It follows that the polynomial operator in the shift which U. Oberst and J. C. Willems have introduced to define time invariant discrete linear dynamical systems can be explained as the adjoint of the polynomial multiplication.
British Journal of Mathematics & Computer Science, Jan 10, 2017
arXiv (Cornell University), May 31, 2019
Journal of Algebra and Related Topics, Dec 1, 2019
![Research paper thumbnail of Finding a Generator Matrix of a Multidimensional Cyclic Code. (arXiv:1906.03491v1 [cs.IT])](https://attachments.academia-assets.com/111403246/thumbnails/1.jpg)
](arXiv (Cornell University), Oct 7, 2019
ArXiv, 2019
A closer look at linear recurring sequences allowed us to define the multiplication of a univaria... more A closer look at linear recurring sequences allowed us to define the multiplication of a univariate polynomial and a sequence, viewed as a power series with another variable, resulting in another sequence. Extending this operation, one gets the multiplication of matrices of multivariate polynomials and vectors of powers series. A dynamical system, according to U. Oberst is then the kernel of the linear mapping of modules defined by a polynomial matrix by this operation. Applying these tools in the decoding of the so-called one point algebraic-geometry codes, after showing that the syndrome array, which is the general transform of the error in a received word is a linear recurring sequence, we construct a dynamical system. We then prove that this array is the solution of Cauchy's homogeneous equations with respect to the dynamical system. The aim of the Berlekamp-Massey-Sakata Algorithm in the decoding process being the determination of the syndrome array, we have proved that in ...
![Research paper thumbnail of Basis of a multicyclic code as an Ideal in F[X_1,...,X_s]/](https://attachments.academia-assets.com/111403247/thumbnails/1.jpg)
](Journal of Algebra and Related Topics, 2018
First, we apply the method presented by Zahra Sepasdar in the two-dimensional case to construct a... more First, we apply the method presented by Zahra Sepasdar in the two-dimensional case to construct a basis of a three dimensional cyclic code. We then generalize this construction to a general sss-dimensional cyclic code.
ArXiv, 2019
We generalize Sepasdar's method for finding a generator matrix of two-dimensional cyclic code... more We generalize Sepasdar's method for finding a generator matrix of two-dimensional cyclic codes to find an independent subset of a general multicyclic code, which may form a basis of the code as a vector subspace. A generator matrix can be then constructed from this basis.
British Journal of Mathematics & Computer Science, 2017
arXiv (Cornell University), Mar 19, 2012
Journal of Algebra and Related Topics, Dec 1, 2017
arXiv (Cornell University), Mar 19, 2012
In this paper, we use a duality between the vector space of the multi-indexed sequences over a fi... more In this paper, we use a duality between the vector space of the multi-indexed sequences over a field and the vector subspace of the sequences with finite support over this field to characterize the closed subpaces of multi-indexed sequences. Then we prove that the polynomial operator in the shift which Oberst and Willems have introduced to define time invariant discrete linear dynamical systems is the adjoint of the polynomial multiplication. We end this paper by describing these systems.
British Journal of Mathematics & Computer Science, 2016
British Journal of Mathematics & Computer Science, 2015
The vector space of the multi-indexed sequences over a field and the vector space of the sequence... more The vector space of the multi-indexed sequences over a field and the vector space of the sequences with finite support are dual to each other, with respect to an appropriate scalar product. It follows that the polynomial operator in the shift which U. Oberst and J. C. Willems have introduced to define time invariant discrete linear dynamical systems can be explained as the adjoint of the polynomial multiplication.
British Journal of Mathematics & Computer Science, Jan 10, 2017
arXiv (Cornell University), May 31, 2019
Journal of Algebra and Related Topics, Dec 1, 2019
arXiv (Cornell University), Oct 7, 2019
ArXiv, 2019
A closer look at linear recurring sequences allowed us to define the multiplication of a univaria... more A closer look at linear recurring sequences allowed us to define the multiplication of a univariate polynomial and a sequence, viewed as a power series with another variable, resulting in another sequence. Extending this operation, one gets the multiplication of matrices of multivariate polynomials and vectors of powers series. A dynamical system, according to U. Oberst is then the kernel of the linear mapping of modules defined by a polynomial matrix by this operation. Applying these tools in the decoding of the so-called one point algebraic-geometry codes, after showing that the syndrome array, which is the general transform of the error in a received word is a linear recurring sequence, we construct a dynamical system. We then prove that this array is the solution of Cauchy's homogeneous equations with respect to the dynamical system. The aim of the Berlekamp-Massey-Sakata Algorithm in the decoding process being the determination of the syndrome array, we have proved that in ...
Journal of Algebra and Related Topics, 2018
First, we apply the method presented by Zahra Sepasdar in the two-dimensional case to construct a... more First, we apply the method presented by Zahra Sepasdar in the two-dimensional case to construct a basis of a three dimensional cyclic code. We then generalize this construction to a general sss-dimensional cyclic code.
ArXiv, 2019
We generalize Sepasdar's method for finding a generator matrix of two-dimensional cyclic code... more We generalize Sepasdar's method for finding a generator matrix of two-dimensional cyclic codes to find an independent subset of a general multicyclic code, which may form a basis of the code as a vector subspace. A generator matrix can be then constructed from this basis.
British Journal of Mathematics & Computer Science, 2017
arXiv (Cornell University), Mar 19, 2012