179 research outputs found

    Characterization and mass formulas of symplectic self-orthogonal and LCD codes and their application

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    The object of this paper is to study two very important classes of codes in coding theory, namely self-orthogonal (SO) and linear complementary dual (LCD) codes under the symplectic inner product, involving characterization, constructions, and their application. Using such a characterization, we determine the mass formulas of symplectic SO and LCD codes by considering the action of the symplectic group, and further obtain some asymptotic results. Finally, under the Hamming distance, we obtain some symplectic SO (resp. LCD) codes with improved parameters directly compared with Euclidean SO (resp. LCD) codes. Under the symplectic distance, we obtain some additive SO (resp. additive complementary dual) codes with improved parameters directly compared with Hermitian SO (resp. LCD) codes. Further, we also construct many good additive codes outperform the best-known linear codes in Grassl's code table. As an application, we construct a number of record-breaking (entanglement-assisted) quantum error-correcting codes, which improve Grassl's code table

    Anticodes and error-correcting for digital data transmission

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    The work reported in this thesis is an investigation in the field of error-control coding. This subject is concerned with increasing the reliability of digital data transmission through a noisy medium, by coding the transmitted data. In this respect, an extension and development of a method for finding optimum and near-optimum codes, using N.m digital arrays known as anticodes, is established and described. The anticodes, which have opposite properties to their complementary related error-control codes, are disjoined fron the original maximal-length code, known as the parent anticode, to leave good linear block codes. The mathematical analysis of the parent anticode and as a result the mathematical analysis of its related anticodes has given some useful insight into the construction of a large number of optimum and near-optimum anticodes resulting respectively in a large number of optimum and near-optimum codes. This work has been devoted to the construction of anticodes from unit basic (small dimension) anticodes by means of various systematic construction and refinement techniques, which simplifies the construction of the associated linear block codes over a wide range of parameters. An extensive list of these anticodes and codes is given in the thesis. The work also has been extended to the construction of anticodes in which the symbols have been chosen from the elements of the finite field GF(q), and, in particular, a large number of optimum and near-optimum codes over GF(3) have been found. This generalises the concept of anticodes into the subject of multilevel codes

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Easily decoded error correcting codes

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    This thesis is concerned with the decoding aspect of linear block error-correcting codes. When, as in most practical situations, the decoder cost is limited an optimum code may be inferior in performance to a longer sub-optimum code' of the same rate. This consideration is a central theme of the thesis. The best methods available for decoding short optimum codes and long B.C.H. codes are discussed, in some cases new decoding algorithms for the codes are introduced. Hashim's "Nested" codes are then analysed. The method of nesting codes which was given by Hashim is shown to be optimum - but it is seen that the codes are less easily decoded than was previously thought. "Conjoined" codes are introduced. It is shown how two codes with identical numbers of information bits may be "conjoined" to give a code with length and minimum distance equal to the sum of the respective parameters of the constituent codes but with the same number of information bits. A very simple decoding algorithm is given for the codes whereby each constituent codeword is decoded and then a decision is made as to the correct decoding. A technique is given for adding more codewords to conjoined codes without unduly increasing the decoder complexity. Lastly, "Array" codes are described. They are formed by making parity checks over carefully chosen patterns of information bits arranged in a two-dimensional array. Various methods are given for choosing suitable patterns. Some of the resulting codes are self-orthogonal and certain of these have parameters close to the optimum for such codes. A method is given for adding more codewords to array codes, derived from a process of augmentation known for product codes

    25th Annual Computational Neuroscience Meeting: CNS-2016

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    Abstracts of the 25th Annual Computational Neuroscience Meeting: CNS-2016 Seogwipo City, Jeju-do, South Korea. 2–7 July 201

    CĂłdigos q-arios autoduales con un automorfismos de orden primo

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    En la teoría clásica de códigos, los códigos autoduales juegan un papel muy importante por su rica estructura algebraica. Para ellos la distancia mínima esta acotada superiormente y se denominan extremales aquellos códigos que alcanzan dicha cota. Estos son particularmente interesantes, ya que ellos pueden corregir el mayor numero de errores entre todos los códigos autoduales. El propósito de este trabajo es analizar la estructura algebraica de un código autodual q-ario con un automorfismo de orden primo distinto a la característica del cuerpo y posteriormente con ello, dar una clasificación de todos los códigos extremales Tipo I y Tipo III de longitud 60 con un automorfismo de orden 29. Para esto hacemos uso de la descomposición del código C como la suma directa de dos subcódigos e implementamos herramientas computacionales sobre todas las posibles matrices del código. Concretamente, demostramos que existen exactamente tres [60, 30, 12] códigos extremales Tipo I y existen tres códigos extremales [60, 30, 18] Tipo III, con un automorfismo de orden 29. como la suma directa de dos subcódigos e implementamos herramientas computacionales sobre todas las posibles matrices del código. Concretamente, demostramos que existen exactamente tres [60, 30, 12] códigos extremales Tipo I y tres códigos extremales [60, 30, 18] Tipo III, con un automorfismo de orden 29.MaestríaMagister en Matemática

    Implication des facteurs génétiques et environnementaux dans la susceptibilité à l'inflammation du système nerveux central

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    La sclérose en plaques (SEP) est une maladie inflammatoire du système nerveux central (SNC) faisant intervenir des facteurs génétiques, épigénétiques et environnementaux. Mes travaux de thèse ont eu pour objectif d'analyser l'implication de deux facteurs génétiques (Themis1 et Vav1) et d'un facteur environnemental (le stress prénatal). Themis1 et Vav1 sont deux molécules de signalisation du récepteur T (TCR) qui jouent un rôle important dans la sélection thymique des thymocytes. Le rôle de Vav1 a largement été étudié dans les LT matures, contrairement à Themis1 dont le rôle reste très peu caractérisé. Des analyses génétiques chez l'Homme indiquent que Themis1 et Vav1 sont des gènes de susceptibilité à la SEP, mais les mécanismes impliqués n'ont pas été élucidés. Mon équipe d'accueil a montré chez la souris dans un modèle d'encéphalomyélite auto-immune expérimentale (EAE) que le variant naturel Vav1R63W induisait une réduction modérée de l'inflammation du SNC, mais rien n'était connu sur le rôle de Themis1 dans cette pathologie. Durant ma thèse, j'ai donc analysé l'implication de Themis1 dans la physiopathologie de l'EAE. De plus, puisque Themis1 et Vav1 interagissent et que Themis1 contrôle positivement l'activation de Vav1, j'ai étudié l'impact de la combinaison de la déficience en Themis1 avec le variant Vav1R63W sur la susceptibilité à l'EAE. J'ai montré que la mutation de Themis1 induit une réduction intermédiaire de la sévérité de l'EAE et que cette réduction est augmentée en présence du variant de Vav1. Mes résultats suggèrent que cela est dépendant d'une réduction de l'encéphalitogénicité des LT conventionnels (Tconv) mutés. La réduction de la signalisation du TCR (notamment de la voie NF-kB) du fait de ces mutations entraine une réduction de la production de cytokines pro-inflammatoires nécessaires à la perturbation de la barrière hémato-encéphalique, et ainsi à l'infiltration du parenchyme cérébral. Ceci résulte chez les souris mutées en une absence d'infiltrat immunitaire dans la moelle épinière. Notre travail souligne ainsi l'intérêt d'analyser la combinaison de plusieurs polymorphismes génétiques ayant un faible poids pour identifier des réseaux moléculaires de susceptibilité à l'auto-immunité qui pourraient expliquer une partie du " missing heritability ". En dehors des facteurs génétiques, les facteurs environnementaux tels que le tabac, l'ensoleillement (vitamine D), ou le microbiote sont aujourd'hui communément admis comme influant la susceptibilité à la SEP. Plusieurs études ont montré que le stress pendant la grossesse (stress prénatal) pouvait avoir des répercussions sur la susceptibilité de la descendance à diverses pathologies psychiatriques, neurologiques ou inflammatoires. Cependant, l'impact du stress prénatal (PS) sur la susceptibilité de la progéniture à l'inflammation du SNC reste très peu étudié. Dans ce contexte, nous avons utilisé un modèle de PS chronique afin d'étudier les répercussions que cela pourrait avoir sur la susceptibilité de la descendance à développer l'EAE. Nous avons montré que les progénitures provenant des femelles stressées développent une EAE moins sévère en comparaison avec les progénitures issues de femelles non stressées. Nos résultats préliminaires montrent que cette réduction est associée à une réduction de l'infiltrat immunitaire dans la moelle épinière, à une augmentation de la fréquence de LT régulateurs, et à une réduction de la production de cytokines pro-inflammatoires. Nos résultats mettent ainsi en évidence qu'avant même la naissance, des facteurs environnementaux extérieurs modulent la susceptibilité à l'inflammation du SNC, possiblement par l'altération des fonctions des LT CD4.Multiple sclerosis (MS) is an inflammatory disease of the central nervous system (CNS) involving genetic, epigenetic, and environmental factors. My PhD work aimed at analyzing the involvement of two genetic factors (Themis1 and Vav1) and of environmental factor (prenatal stress) in susceptibility to CNS inflammation and to decipher the mechanisms involved. Themis1 and Vav1 are two T receptor (TCR) signaling molecules that play an important role in thymic selection of thymocytes. Genetic analyzes in humans indicate that Themis1 and Vav1 are MS susceptibility genes, but the mechanisms involved have not been elucidated. Although the role of Vav1 has been widely studied in mature T cells, the role of Themis1 remains, however, poorly characterized. Previous work from my team using the experimental autoimmune encephalomyelitis (EAE) mice model of MS showed that the natural variant Vav1R63W induced a moderate reduction of CNS inflammation, but the role of Themis1 in this pathology was still unknown. During my PhD, I therefore analyzed the involvement of Themis1 in the pathophysiology of EAE. Moreover, since Themis1 and Vav1 interact together and Themis1 positively controls the activation of Vav1, I studied the impact of the combination of Themis1 deficiency with the Vav1R63W variant on EAE susceptibility. I have shown that Themis1 deletion induces an intermediate reduction of EAE severity, and that this reduction is increased in the presence of the Vav1 variant. My results suggest that this is dependent on a reduction in the encephalitogenicity of mutated conventional T cells (Tconv). The reduction in TCR signaling (in particular the NF-kB pathway) due to these mutations leads to a reduction in the production of pro-inflammatory cytokines necessary for the disruption of the blood-brain barrier, and thus for the infiltration of the cerebral parenchyma, resulting in the absence of immune infiltrate in the spinal cord of mutated mice. Our work therefore underlines the interest of analyzing the combination of several genetic polymorphisms having a low weight to identify molecular networks of susceptibility to autoimmunity which could explain part of the "missing heritability". Besides genetic factors, environmental factors such as tobacco, sunlight (vitamin D), or the microbiota are now commonly accepted as influencing susceptibility to MS. Several studies have shown that stress during pregnancy (prenatal stress) could have repercussions on the susceptibility of offspring to various psychiatric, neurological, or inflammatory pathologies. However, the impact of prenatal stress (PS) on offspring susceptibility to CNS inflammation remains poorly studied. In this context, we used a model of chronic PS to study the repercussions that it could have on offspring susceptibility to develop EAE. We have shown that offspring from stressed females develop a less severe EAE compared to offspring from unstressed females. Our preliminary results show that this reduction is associated with a reduction in the immune infiltrate in the spinal cord, an increase in the frequency of regulatory T cells, and a reduction in the production of pro-inflammatory cytokines. Our results thus show that even before birth, external environmental factors modulate the susceptibility to CNS inflammation, possibly by altering CD4 T cell function

    Proceedings of the Fourth Russian Finnish Symposium on Discrete Mathematics

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