Papers by Edgar Martinez-Moro
Applicable Algebra in Engineering, Communication and Computing, Jun 22, 2023
In this work we present a standard model for Galois rings based on the standard model of their re... more In this work we present a standard model for Galois rings based on the standard model of their residual fields, that is, a a sequence of Galois rings starting with Zpr that coves all the Galois rings with that characteristic ring and such that there is an algorithm producing each member of the sequence whose input is the size of the required ring.
Designs, Codes and Cryptography, 2020
Linear complementary dual (LCD) codes and linear complementary pair (LCP) of codes over finite fi... more Linear complementary dual (LCD) codes and linear complementary pair (LCP) of codes over finite fields have been intensively studied recently due to their applications in cryptography, in the context of side channel and fault injection attacks. The security parameter for an LCP of codes (C, D) is defined as the minimum of the minimum distances d(C) and d(D ⊥). It has been recently shown that if C and D are both 2-sided group codes over a finite field, then C and D ⊥ are permutation equivalent. Hence the security parameter for an LCP of 2-sided group codes (C, D) is simply d(C). We extend this result to 2-sided group codes over finite chain rings.
Finite Fields and Their Applications, 2022
In this paper, a transform approach is used for polycyclic and serial codes over finite local rin... more In this paper, a transform approach is used for polycyclic and serial codes over finite local rings in the case that the defining polynomials have no multiple roots. This allows us to study them in terms of linear algebra and invariant subspaces as well as understand the duality in terms of the transform domain. We also make a characterization of when two polycyclic ambient spaces are Hamming-isometric.
Designs, Codes and Cryptography, 2020
A locally recoverable code is an error-correcting code such that any erasure in a single coordina... more A locally recoverable code is an error-correcting code such that any erasure in a single coordinate of a codeword can be recovered from a small subset of other coordinates. In this article we develop an algorithm that computes a recovery structure as concise posible for an arbitrary linear code C and a recovery method that realizes it. This algorithm also provides the locality and the dual distance of C. Complexity issues are studied as well. Several examples are included.
Discrete Mathematics, 2018
Additive cyclic codes over Galois rings were investigated in [3]. In this paper, we investigate t... more Additive cyclic codes over Galois rings were investigated in [3]. In this paper, we investigate the same problem but over a more general ring family, finite commutative chain rings. When we focus on non-Galois finite commutative chain rings, we observe two different kinds of additivity. One of them is a natural generalization of the study in [3], whereas the other one has some unusual properties especially while constructing dual codes. We interpret the reasons of such properties and illustrate our results giving concrete examples.
We show the combinatorial structure of Z² modulo sublattices similar to Z². The tool we use for d... 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.
2010 IEEE Information Theory Workshop, 2010
There are two gradient descent decoding procedures for binary codes proposed independently by Lie... more There are two gradient descent decoding procedures for binary codes proposed independently by Liebler and by Ashikhmin and Barg. Liebler in his paper [15] mentions that both algorithms have the same philosophy but in fact they are rather different. The purpose of this communication is to show that both algorithms can be seen as two ways of understanding the reduction process algebraic monoid structure related to the code. The main tool used for showing this is the Gröbner representation of the monoid associated to the linear code.
mac.cie.uva.es
Page 1. Ciclos, ideales y códigos binarios Borges-Quintana, M.(a)*;Borges-Trenard, MA(a); Fitzpat... more 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 ...
IEEE Transactions on Information Theory, 2019
In this paper we show some applications of algebraic curves to the construction of kernels of pol... more In this paper we show some applications of algebraic curves to the construction of kernels of polar codes over a discrete memoryless channel which is symmetric w.r.t the field operations. We will also study the minimum distance of the polar codes proposed, their duals and the exponents of the matrices used for defining them. All the restrictions that we make to our curves will be accomplished by the so called Castle Curves.
ArXiv, 2021
A Private Information Retrieval (PIR) scheme allows users to retrieve data from a database withou... 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.
Journal of Pure and …, 2006
We present a Gröbner basis associated with the symmetric group of degree n, which is determined b... more We present a Gröbner basis associated with the symmetric group of degree n, which is determined by a strong generating set of the symmetric group and is defined by means of a term ordering with the elimination property.
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Libro De Resumenes Del Xiii Encuentro De Algebra Computacional Y Aplicaciones Eaca2012 2012 Isbn 978 84 8138 770 4 Pags 127 130, 2012
Eaca 2010 Xii Encuentro De Algebra Computacional Y Aplicaciones 12th Meeting on Computer Algebra and Applications Libro De Resumenes Book of Abstracts Santiago De Compostela 19 21 De Julio De 2010 2010 Isbn 978 84 9887 518 8 Pags 55 60, 2010
Criptologia Y Seguridad De La Informacion Actas De La Vi Reunion Espanola Sobre Criptologia Y Seguridad De La Informacion Vi Recsi Tenerife Islas Canarias 14 16 Septiembre De 2000 2000 Isbn 84 7897 431 8 Pags 145 150, 2000
Información del artículo Una revisión de las premisas en esquemas visuales para compartir secretos.
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Papers by Edgar Martinez-Moro