This dissertation studies problems of data management under unreliable conditions: how can data be efficiently reconstructed, synchronized, transmitted, and stored in the presence of uncertainty or noise? The common underlying thread running through the approaches to these problems is the discipline of coding theory. Problems related to data editin...
This dissertation studies problems of data management under unreliable conditions: how can data be efficiently reconstructed, synchronized, transmitted, and stored in the presence of uncertainty or noise? The common underlying thread running through the approaches to these problems is the discipline of coding theory. Problems related to data editin...
This dissertation studies problems of data management under unreliable conditions: how can data be efficiently reconstructed, synchronized, transmitted, and stored in the presence of uncertainty or noise? The common underlying thread running through the approaches to these problems is the discipline of coding theory. Problems related to data editin...
This dissertation studies problems of data management under unreliable conditions: how can data be efficiently reconstructed, synchronized, transmitted, and stored in the presence of uncertainty or noise? The common underlying thread running through the approaches to these problems is the discipline of coding theory. Problems related to data editin...
This dissertation studies problems of data management under unreliable conditions: how can data be efficiently reconstructed, synchronized, transmitted, and stored in the presence of uncertainty or noise? The common underlying thread running through the approaches to these problems is the discipline of coding theory. Problems related to data editin...
Given a linear code C, one can define the dth power of C as the span of all componentwise products of d elements of C. A power of C may quickly fill the whole space. Our purpose is to answer the following question: does the square of a code typically fill the whole space? We give a positive answer, for codes of dimension k and length roughly (1/2)k...
Les techniques de chiffrement les plus utilisées en cryptographie, basées sur des problèmes de théorie des nombres, présentent malgré leur efficacité des défauts notamment une vulnérabilité aux attaques menées à l'aide d'ordinateur quantiques. Il est donc pertinent d'étudier d'autres familles de cryptosystèmes. Nous nous intéressons ici aux cryptos...
Cette thèse porte sur les problèmes algorithmiques qui apparaissent lorsque l’onsouhaite mettre en œuvre un cryptosystème basé sur un code correcteur d’erreur oubien une cryptanalyse d’un tel système. L’intérêt de ces système provient de leurexcellente complexité algorithmique, meilleure de plusieurs ordres de grandeurs entermes de complexité que l...
10.1016/j.tcs.2013.09.008 / Theoretical Computer Science / 520 / 51-61 / TCSCD
Published in Discrete Mathematics
Coordinate i of an error-correcting code has locality r if its value is determined by some r other coordinates. Recently an optimal trade-off between information locality of linear codes, code distance, and redundancy has been obtained. Furthermore, for linear codes meeting this trade-off, structure theorems were derived. In this work we generalize...
