Squares of matrix-product codes

The component-wise or Schur product $C*C'$ of two linear error-correcting codes $C$ and $C'$ over certain finite field is the linear code spanned by all component-wise products of a codeword in $C$ with a codeword in $C'$. When $C=C'$, we call the product the square of $C$ and denote it $C^{*2}$. Motivated by several applications of squares of linear codes in the area of cryptography, in this paper we study squares of so-called matrix-product codes, a general construction that allows to obtain new longer codes from several ``constituent'' codes. We show that in many cases we can relate the square of a matrix-product code to the squares and products of their constituent codes, which allow us to give bounds or even determine its minimum distance. We consider the well-known $(u,u+v)$-construction, or Plotkin sum (which is a special case of a matrix-product code) and determine which parameters we can obtain when the constituent codes are certain cyclic codes. In addition, we use the same techniques to study the squares of other matrix-product codes, for example when the defining matrix is Vandermonde (where the minimum distance is in a certain sense maximal with respect to matrix-product codes).This work is supported by the Danish Council for IndependentResearch: grant DFF-4002-00367, theSpanish Ministry of Economy/FEDER: grant RYC-2016-20208 (AEI/FSE/UE), the Spanish Ministry of Science/FEDER: grant PGC2018-096446-B-C21, and Junta de CyL (Spain): grant VA166G

On squares of cyclic codes

The square $C^{*2}$ of a linear error correcting code $C$ is the linear code spanned by the component-wise products of every pair of (non-necessarily distinct) words in $C$. Squares of codes have gained attention for several applications mainly in the area of cryptography, and typically in those applications one is concerned about some of the parameters (dimension, minimum distance) of both $C^{*2}$ and $C$. In this paper, motivated mostly by the study of this problem in the case of linear codes defined over the binary field, squares of cyclic codes are considered. General results on the minimum distance of the squares of cyclic codes are obtained and constructions of cyclic codes $C$ with relatively large dimension of $C$ and minimum distance of the square $C^{*2}$ are discussed. In some cases, the constructions lead to codes $C$ such that both $C$ and $C^{*2}$ simultaneously have the largest possible minimum distances for their length and dimensions.Comment: Accepted at IEEE Transactions on Information Theory. IEEE early access version available at https://ieeexplore.ieee.org/document/8451926

"Vikingland" and the Epic of Emigration

El artículo versa sobre la construcción de la identidad cultural gallega desde lo audiovisual, tomando como punto de referencia Vikingland (2011) de Xurxo Chirro. El propósito es explorar los lugares comunes del fenómeno migratorio comparando este filme con obras afines como Mamasunción (1984) o Avión, el pueblo ausente (2011), con el objetivo de conformar un depósito visual de nuestra memoria colectiva.O artigo versa sobre a construción da identidade cultural galega desde o audiovisual, tomando como punto de referencia Vikingland (2011) de Xurxo Chirro. O propósito é explorar os lugares comúns do fenómeno migratorio comparando este filme con obras afíns como Mamasunción (1984) ou Avión, el pueblo ausente (2011), co obxectivo de conformar un depósito visual da nosa memoria colectiva.This article focuses on the construction of cultural identity through Galician audiovisual production, taking the film Vikingland (2011) by Xurxo Chirro as a reference. The purpose of this study is to explore the leitmotifs of the migratory phenomenon by comparing this production with other related works such as Mamasunción or Avión, el pueblo ausente in order to build a visual repository of Galician collective memory

T. De Mauro: Grande Dizionario Italiano dell´Uso. Torino, UTET, 1999

Sin resume

Efficient UC Commitment Extension with Homomorphism for Free (and Applications)

Homomorphic universally composable (UC) commitments allow for the sender to reveal the result of additions and multiplications of values contained in commitments without revealing the values themselves while assuring the receiver of the correctness of such computation on committed values. In this work, we construct essentially optimal additively homomorphic UC commitments from any (not necessarily UC or homomorphic) extractable commitment. We obtain amortized linear computational complexity in the length of the input messages and rate 1. Next, we show how to extend our scheme to also obtain multiplicative homomorphism at the cost of asymptotic optimality but retaining low concrete complexity for practical parameters. While the previously best constructions use UC oblivious transfer as the main building block, our constructions only require extractable commitments and PRGs, achieving better concrete efficiency and offering new insights into the sufficient conditions for obtaining homomorphic UC commitments. Moreover, our techniques yield public coin protocols, which are compatible with the Fiat-Shamir heuristic. These results come at the cost of realizing a restricted version of the homomorphic commitment functionality where the sender is allowed to perform any number of commitments and operations on committed messages but is only allowed to perform a single batch opening of a number of commitments. Although this functionality seems restrictive, we show that it can be used as a building block for more efficient instantiations of recent protocols for secure multiparty computation and zero knowledge non-interactive arguments of knowledge

Strutturazione testuale in italiano e in danese, edic. De Gunver Skytte, Iorn Korzen, Paola Polito y Erling Strudsholm. Copenhague, Museum Tusculanums Forlag, 1999.

Sin resume

La mística de la feminidad en Mad Men

El artículo trata de desvelar alguna de las claves de la serie televisiva Mad Men contrastándola con la obra de Betty Friedan La mística de la feminidad. Ambas inciden en el papel que desempeña la mujer a comienzos de la década de los sesenta del pasado siglo, en el contexto de la cultura de masas, con la sociedad de consumo y la publicidad como rasgos definitorios. Betty Draper, uno de los personajes principales de Mad Men, representa el paradigma de la mística de la feminidad, ya que muestra todos los síntomas propios de las mujeres de clase media de su época, que se consagran a las labores domésticas a pesar de haber logrado sus derechos políticos y civiles ya antes de la Segunda Guerra Mundial. Analizando las pautas de conducta de Betty Draper se comprenden los mecanismos sociales y culturales que motivan esa involución, frenando el acceso de la mujer a la esfera profesional. Así mismo se abordará el estigma que supone el concepto de mujer de carrera, introducido a través de otros personajes como Peggy Olson o Joan Holloway, para mostrar los diferentes niveles de dependencia femenina de los convencionalismos sociales según sean las circunstancias particulares de cada mujer

Torsion Limits and Riemann-Roch Systems for Function Fields and Applications

The Ihara limit (or -constant) $A(q)$ has been a central problem of study in the asymptotic theory of global function fields (or equivalently, algebraic curves over finite fields). It addresses global function fields with many rational points and, so far, most applications of this theory do not require additional properties. Motivated by recent applications, we require global function fields with the additional property that their zero class divisor groups contain at most a small number of $d$-torsion points. We capture this by the torsion limit, a new asymptotic quantity for global function fields. It seems that it is even harder to determine values of this new quantity than the Ihara constant. Nevertheless, some non-trivial lower- and upper bounds are derived. Apart from this new asymptotic quantity and bounds on it, we also introduce Riemann-Roch systems of equations. It turns out that this type of equation system plays an important role in the study of several other problems in areas such as coding theory, arithmetic secret sharing and multiplication complexity of finite fields etc. Finally, we show how our new asymptotic quantity, our bounds on it and Riemann-Roch systems can be used to improve results in these areas.Comment: Accepted for publication in IEEE Transactions on Information Theory. This is an extended version of our paper in Proceedings of 31st Annual IACR CRYPTO, Santa Barbara, Ca., USA, 2011. The results in Sections 5 and 6 did not appear in that paper. A first version of this paper has been widely circulated since November 200

Improved Bounds on the Threshold Gap in Ramp Secret Sharing

Producción CientíficaAbstract: In this paper we consider linear secret sharing schemes over a finite field Fq, where the secret is a vector in Fℓq and each of the n shares is a single element of Fq. We obtain lower bounds on the so-called threshold gap g of such schemes, defined as the quantity r−t where r is the smallest number such that any subset of r shares uniquely determines the secret and t is the largest number such that any subset of t shares provides no information about the secret. Our main result establishes a family of bounds which are tighter than previously known bounds for ℓ≥2. Furthermore, we also provide bounds, in terms of n and q, on the partial reconstruction and privacy thresholds, a more fine-grained notion that considers the amount of information about the secret that can be contained in a set of shares of a given size. Finally, we compare our lower bounds with known upper bounds in the asymptotic setting.Danish Council for Independent Research (grant DFF-4002- 00367)Ministerio de Economía, Industria y Competitividad (grants MTM2015-65764-C3-2-P / MTM2015-69138- REDT)RYC-2016-20208 (AEI/FSE/UE)Junta de Castilla y León (grant VA166G18