Ivan Bailera
University of Zaragoza, Matemática Aplicada, Department Member
La memoria a largo plazo es fundamental para tener una base de conocimiento sólida sobre la que construir nuevos modelos mentales. Sin embargo, los estudiantes a menudo estudian de forma masiva e inmediata, centrándose únicamente en... more
La memoria a largo plazo es fundamental para tener una base de conocimiento sólida sobre la que construir nuevos modelos mentales. Sin embargo, los estudiantes a menudo estudian de forma masiva e inmediata, centrándose únicamente en superar las pruebas de evaluación. La "curva de olvido" (Herman Ebbinghaus, 1885) muestra que la pérdida de retención a lo largo del tiempo tiene un decaimiento exponencial cuando no se hace ningún esfuerzo por revisar la información. Si se repasa lo aprendido en el momento adecuado y se utilizan herramientas de aprendizaje activo, se reduce la tasa de olvido, haciendo que el tiempo necesario entre repasos consecutivos sea cada vez más largo, hasta que finalmente la información se fija en la memoria a largo plazo.Esta metodología que aplana la curva de olvido a través de la Repetición Espaciada se ha utilizado con éxito en el estudio de lenguas extranjeras debido a su alto rendimiento. El trabajo aquí presentado tiene como objetivo trasladar el...
We introduce the Hadamard full propelinear codes that factorize as direct product of groups such that their associated group is $C_{2t}\times C_2$. We study the rank, the dimension of the kernel, and the structure of these codes. For... more
We introduce the Hadamard full propelinear codes that factorize as direct product of groups such that their associated group is $C_{2t}\times C_2$. We study the rank, the dimension of the kernel, and the structure of these codes. For several specific parameters we establish some links from circulant Hadamard matrices and the nonexistence of the codes we study. We prove that the dimension of the kernel of these codes is bounded by 3 if the code is nonlinear. We also get an equivalence between circulant complex Hadamard matrix and a type of Hadamard full propelinear code, and we find a new example of circulant complex Hadamard matrix of order 16.
Research Interests:
In this paper we study Butson Hadamard matrices, and codes over finite rings coming from these matrices in logarithmic form, called BH-codes. We introduce a new morphism of Butson Hadamard matrices through a generalized Gray map on the... more
In this paper we study Butson Hadamard matrices, and codes over finite rings coming from these matrices in logarithmic form, called BH-codes. We introduce a new morphism of Butson Hadamard matrices through a generalized Gray map on the matrices in logarithmic form, which is comparable to the morphism given in a recent note of O Cathain and Swartz. That is, we show how, if given a Butson Hadamard matrix over the $k^{\rm th}$ roots of unity, we can construct a larger Butson matrix over the $\ell^{\rm th}$ roots of unity for any $\ell$ dividing $k$, provided that any prime $p$ dividing $k$ also divides $\ell$. We prove that a $\mathbb{Z}_{p^s}$-additive code with $p$ a prime number is isomorphic as a group to a BH-code over $\mathbb{Z}_{p^s}$ and the image of this BH-code under the Gray map is a BH-code over $\mathbb{Z}_p$ (binary Hadamard code for $p=2$). Further, we investigate the inherent propelinear structure of these codes (and their images) when the Butson matrix is cocyclic. So...
Research Interests:
Codes from generalized Hadamard matrices have already been introduced. Here we deal with these codes when the generalized Hadamard matrices are cocyclic. As a consequence, a new class of codes that we call generalized Hadamard full... more
Codes from generalized Hadamard matrices have already been introduced. Here we deal with these codes when the generalized Hadamard matrices are cocyclic. As a consequence, a new class of codes that we call generalized Hadamard full propelinear codes turns out. We prove that their existence is equivalent to the existence of central relative $(v,w,v,v/w)$-difference sets. Moreover, some structural properties of these codes are studied and examples are provided.
Research Interests:
In this paper, we give a characterization of quasi-Hadamard groups in terms of propelinear codes. We define a new class of codes that we call quasi-Hadamard full propelinear codes. Some structural properties of these codes are studied and... more
In this paper, we give a characterization of quasi-Hadamard groups in terms of propelinear codes. We define a new class of codes that we call quasi-Hadamard full propelinear codes. Some structural properties of these codes are studied and examples are provided.
Research Interests:
We introduce the Hadamard full propelinear codes that factorize as direct product of groups such that their associated group is $C_{2t} \times C_2$. We study the rank, the dimension of the kernel, and the structure of these codes. For... more
We introduce the Hadamard full propelinear codes that factorize as direct product of groups such that their associated group is $C_{2t} \times C_2$. We study the rank, the dimension of the kernel, and the structure of these codes. For several specific parameters we establish some links from circulant Hadamard matrices and the nonexistence of the codes we study. We prove that the dimension of the kernel of these codes is bounded by 3 if the code is nonlinear. We also get an equivalence between circulant complex Hadamard matrix and a type of Hadamard full propelinear code, and we find a new example of circulant complex Hadamard matrix of order 16.
Research Interests:
A new subclass of Hadamard full propelinear codes is introduced in this article. We define the HFP(2t, 2, 2)-codes as codes with a group structure isomorphic to C2t × C2 x C2. Concepts such as rank and dimension of the kernel are studied,... more
A new subclass of Hadamard full propelinear codes is introduced in this article. We define the HFP(2t, 2, 2)-codes as codes with a group structure isomorphic to C2t × C2 x C2. Concepts such as rank and dimension of the kernel are studied, and bounds for them are established. For t odd, r = 4t − 1 and k = 1. For t even, r ≤ 2t and k = 2, and r = 2t if and only if t ≡ 0 (mod 4).
Research Interests:
Research Interests:
In this paper we study Butson Hadamard matrices, and codes over finite rings coming from these matrices in logarithmic form, called BH-codes. We introduce a new morphism of Butson Hadamard matrices through a generalized Gray map on the... more
In this paper we study Butson Hadamard matrices, and codes over finite rings coming from these matrices in logarithmic form, called BH-codes. We introduce a new morphism of Butson Hadamard matrices through a generalized Gray map on the matrices in logarithmic form, which is comparable to the morphism given in a recent note of Ó Catháin and Swartz. That is, we show how, if given a Butson Ha-damard matrix over the k th roots of unity, we can construct a larger Butson matrix over the ℓ th roots of unity for any ℓ dividing k, provided that any prime p dividing k also divides ℓ. We prove that a Z p s-additive code with p a prime number is isomor-phic as a group to a BH-code over Z p s and the image of this BH-code under the Gray map is a BH-code over Z p (binary Hadamard code for p = 2). Further, we investigate the inherent propelinear structure of these codes (and their images) when the Butson matrix is cocyclic. Some structural properties of these codes are studied and examples are provided.
Research Interests:
Codes from generalized Hadamard matrices have already been introduced. Here we deal with these codes when the generalized Hada-mard matrices are cocyclic. As a consequence, a new class of codes that we call generalized Hadamard full... more
Codes from generalized Hadamard matrices have already been introduced. Here we deal with these codes when the generalized Hada-mard matrices are cocyclic. As a consequence, a new class of codes that we call generalized Hadamard full propelinear codes turns out. We prove that their existence is equivalent to the existence of central relative (v, w, v, v/w)-difference sets. Moreover, some structural properties of these codes are studied and examples are provided.