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Título : Codes: An Introduction to Information Communication and Cryptography Tipo de documento: documento electrónico Autores: N.L. Biggs ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2008 Colección: Springer Undergraduate Mathematics Series, ISSN 1615-2085 Número de páginas: X, 274 p. 36 illus Il.: online resource ISBN/ISSN/DL: 978-1-84800-273-9 Idioma : Inglés (eng) Palabras clave: Computer science Data structures (Computer science) Coding theory Information Number Combinatorics Electrical engineering Science and Theory Communications Engineering, Networks Communication, Circuits Structures, Cryptology Clasificación: 51 Matemáticas Resumen: Information is an important feature of the modern world. Mathematical techniques underlie the devices that we use to handle it, for example, mobile phones, digital cameras, and personal computers. This book is an integrated introduction to the mathematics of coding, that is, replacing information expressed in symbols, such as a natural language or a sequence of bits, by another message using (possibly) different symbols. There are three main reasons for doing this: economy, reliability, and security, and each is covered in detail. Only a modest mathematical background is assumed, the mathematical theory being introduced at a level that enables the basic problems to be stated carefully, but without unnecessary abstraction. Other features include: clear and careful exposition of fundamental concepts, including optimal coding, data compression, and public-key cryptography; concise but complete proofs of results; coverage of recent advances of practical interest, for example in encryption standards, authentication schemes, and elliptic curve cryptography; numerous examples and exercises, and a full solutions manual available to lecturers from www.springer.com This modern introduction to all aspects of coding is suitable for advanced undergraduate or postgraduate courses in mathematics, computer science, electrical engineering, or informatics. It is also useful for researchers and practitioners in related areas of science, engineering and economics Nota de contenido: Coding and its uses -- Prefix free codes -- Economical coding -- Data compression -- Noisy channels -- The problem of reliable communication -- The noisy coding theorems -- Linear codes -- Algebraic coding theory -- Coding natural languages -- The development of cryptography -- Cryptography in theory and practice -- The RSA cryptosystem -- Cryptography and calculation -- Elliptic curve cryptography En línea: http://dx.doi.org/10.1007/978-1-84800-273-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34306 Codes: An Introduction to Information Communication and Cryptography [documento electrónico] / N.L. Biggs ; SpringerLink (Online service) . - London : Springer London, 2008 . - X, 274 p. 36 illus : online resource. - (Springer Undergraduate Mathematics Series, ISSN 1615-2085) .
ISBN : 978-1-84800-273-9
Idioma : Inglés (eng)
Palabras clave: Computer science Data structures (Computer science) Coding theory Information Number Combinatorics Electrical engineering Science and Theory Communications Engineering, Networks Communication, Circuits Structures, Cryptology Clasificación: 51 Matemáticas Resumen: Information is an important feature of the modern world. Mathematical techniques underlie the devices that we use to handle it, for example, mobile phones, digital cameras, and personal computers. This book is an integrated introduction to the mathematics of coding, that is, replacing information expressed in symbols, such as a natural language or a sequence of bits, by another message using (possibly) different symbols. There are three main reasons for doing this: economy, reliability, and security, and each is covered in detail. Only a modest mathematical background is assumed, the mathematical theory being introduced at a level that enables the basic problems to be stated carefully, but without unnecessary abstraction. Other features include: clear and careful exposition of fundamental concepts, including optimal coding, data compression, and public-key cryptography; concise but complete proofs of results; coverage of recent advances of practical interest, for example in encryption standards, authentication schemes, and elliptic curve cryptography; numerous examples and exercises, and a full solutions manual available to lecturers from www.springer.com This modern introduction to all aspects of coding is suitable for advanced undergraduate or postgraduate courses in mathematics, computer science, electrical engineering, or informatics. It is also useful for researchers and practitioners in related areas of science, engineering and economics Nota de contenido: Coding and its uses -- Prefix free codes -- Economical coding -- Data compression -- Noisy channels -- The problem of reliable communication -- The noisy coding theorems -- Linear codes -- Algebraic coding theory -- Coding natural languages -- The development of cryptography -- Cryptography in theory and practice -- The RSA cryptosystem -- Cryptography and calculation -- Elliptic curve cryptography En línea: http://dx.doi.org/10.1007/978-1-84800-273-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34306 Ejemplares
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Título : Selected Unsolved Problems in Coding Theory Tipo de documento: documento electrónico Autores: Joyner, David ; SpringerLink (Online service) ; Kim, Jon-Lark Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2011 Colección: Applied and Numerical Harmonic Analysis Número de páginas: XII, 248 p. 17 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-8256-9 Idioma : Inglés (eng) Palabras clave: Mathematics Coding theory Algebraic geometry Applied mathematics Engineering Information Number and Communication, Circuits Theory Signal, Image Speech Processing Applications of Geometry Clasificación: 51 Matemáticas Resumen: Using an original mode of presentation and emphasizing the computational nature of the subject, this book explores a number of the unsolved problems that continue to exist in coding theory. A well-established and still highly relevant branch of mathematics, the theory of error-correcting codes is concerned with reliably transmitting data over a ‘noisy’ channel. Despite its frequent use in a range of contexts—the first close-up pictures of the surface of Mars, taken by the NASA spacecraft Mariner 9, were transmitted back to Earth using a Reed–Muller code—the subject contains interesting problems that have to date resisted solution by some of the most prominent mathematicians of recent decades. Employing SAGE—a free open-source mathematics software system—to illustrate their ideas, the authors begin by providing background on linear block codes and introducing some of the special families of codes explored in later chapters, such as quadratic residue and algebraic-geometric codes. Also surveyed is the theory that intersects self-dual codes, lattices, and invariant theory, which leads to an intriguing analogy between the Duursma zeta function and the zeta function attached to an algebraic curve over a finite field. The authors then examine a connection between the theory of block designs and the Assmus–Mattson theorem and scrutinize the knotty problem of finding a non-trivial estimate for the number of solutions over a finite field to a hyperelliptic polynomial equation of "small" degree, as well as the best asymptotic bounds for a binary linear block code. Finally, some of the more mysterious aspects relating modular forms and algebraic-geometric codes are discussed. Selected Unsolved Problems in Coding Theory is intended for graduate students and researchers in algebraic coding theory, especially those who are interested in finding current unsolved problems. Familiarity with concepts in algebra, number theory, and modular forms is assumed. The work may be used as supplementary reading material in a graduate course on coding theory or for self-study Nota de contenido: Preface -- Background -- Codes and Lattices -- Kittens and Blackjack -- RH and Coding Theory -- Hyperelliptic Curves and QR Codes -- Codes from Modular Curves -- Appendix -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-0-8176-8256-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33112 Selected Unsolved Problems in Coding Theory [documento electrónico] / Joyner, David ; SpringerLink (Online service) ; Kim, Jon-Lark . - Boston : Birkhäuser Boston, 2011 . - XII, 248 p. 17 illus : online resource. - (Applied and Numerical Harmonic Analysis) .
ISBN : 978-0-8176-8256-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Coding theory Algebraic geometry Applied mathematics Engineering Information Number and Communication, Circuits Theory Signal, Image Speech Processing Applications of Geometry Clasificación: 51 Matemáticas Resumen: Using an original mode of presentation and emphasizing the computational nature of the subject, this book explores a number of the unsolved problems that continue to exist in coding theory. A well-established and still highly relevant branch of mathematics, the theory of error-correcting codes is concerned with reliably transmitting data over a ‘noisy’ channel. Despite its frequent use in a range of contexts—the first close-up pictures of the surface of Mars, taken by the NASA spacecraft Mariner 9, were transmitted back to Earth using a Reed–Muller code—the subject contains interesting problems that have to date resisted solution by some of the most prominent mathematicians of recent decades. Employing SAGE—a free open-source mathematics software system—to illustrate their ideas, the authors begin by providing background on linear block codes and introducing some of the special families of codes explored in later chapters, such as quadratic residue and algebraic-geometric codes. Also surveyed is the theory that intersects self-dual codes, lattices, and invariant theory, which leads to an intriguing analogy between the Duursma zeta function and the zeta function attached to an algebraic curve over a finite field. The authors then examine a connection between the theory of block designs and the Assmus–Mattson theorem and scrutinize the knotty problem of finding a non-trivial estimate for the number of solutions over a finite field to a hyperelliptic polynomial equation of "small" degree, as well as the best asymptotic bounds for a binary linear block code. Finally, some of the more mysterious aspects relating modular forms and algebraic-geometric codes are discussed. Selected Unsolved Problems in Coding Theory is intended for graduate students and researchers in algebraic coding theory, especially those who are interested in finding current unsolved problems. Familiarity with concepts in algebra, number theory, and modular forms is assumed. The work may be used as supplementary reading material in a graduate course on coding theory or for self-study Nota de contenido: Preface -- Background -- Codes and Lattices -- Kittens and Blackjack -- RH and Coding Theory -- Hyperelliptic Curves and QR Codes -- Codes from Modular Curves -- Appendix -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-0-8176-8256-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33112 Ejemplares
Signatura Medio Ubicación Sub-localización Sección Estado ningún ejemplar Topics in Geometry, Coding Theory and Cryptography / SpringerLink (Online service) ; Arnaldo Garcia ; Stichtenoth, Henning (2007)
Título : Topics in Geometry, Coding Theory and Cryptography Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Arnaldo Garcia ; Stichtenoth, Henning Editorial: Dordrecht : Springer Netherlands Fecha de publicación: 2007 Colección: Algebra and Applications, ISSN 1572-5553 num. 6 Número de páginas: X, 201 p Il.: online resource ISBN/ISSN/DL: 978-1-4020-5334-4 Idioma : Inglés (eng) Palabras clave: Mathematics Data encryption (Computer science) Coding theory Algebraic geometry Number Theory Geometry and Information Encryption Clasificación: 51 Matemáticas Resumen: The theory of algebraic function fields over finite fields has its origins in number theory. However, after Goppa`s discovery of algebraic geometry codes around 1980, many applications of function fields were found in different areas of mathematics and information theory, such as coding theory, sphere packings and lattices, sequence design, and cryptography. The use of function fields often led to better results than those of classical approaches. This book presents survey articles on some of these new developments. Most of the material is directly related to the interaction between function fields and their various applications; in particular the structure and the number of rational places of function fields are of great significance. The topics focus on material which has not yet been presented in other books or survey articles. Wherever applications are pointed out, a special effort has been made to present some background concerning their use En línea: http://dx.doi.org/10.1007/1-4020-5334-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34574 Topics in Geometry, Coding Theory and Cryptography [documento electrónico] / SpringerLink (Online service) ; Arnaldo Garcia ; Stichtenoth, Henning . - Dordrecht : Springer Netherlands, 2007 . - X, 201 p : online resource. - (Algebra and Applications, ISSN 1572-5553; 6) .
ISBN : 978-1-4020-5334-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Data encryption (Computer science) Coding theory Algebraic geometry Number Theory Geometry and Information Encryption Clasificación: 51 Matemáticas Resumen: The theory of algebraic function fields over finite fields has its origins in number theory. However, after Goppa`s discovery of algebraic geometry codes around 1980, many applications of function fields were found in different areas of mathematics and information theory, such as coding theory, sphere packings and lattices, sequence design, and cryptography. The use of function fields often led to better results than those of classical approaches. This book presents survey articles on some of these new developments. Most of the material is directly related to the interaction between function fields and their various applications; in particular the structure and the number of rational places of function fields are of great significance. The topics focus on material which has not yet been presented in other books or survey articles. Wherever applications are pointed out, a special effort has been made to present some background concerning their use En línea: http://dx.doi.org/10.1007/1-4020-5334-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34574 Ejemplares
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Título : Entropy, Search, Complexity Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Csiszár, Imre ; Katona, Gyula O. H ; Tardos, Gábor ; Wiener, Gábor Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2007 Colección: Bolyai Society Mathematical Studies, ISSN 1217-4696 num. 16 Número de páginas: VI, 262 p Il.: online resource ISBN/ISSN/DL: 978-3-540-32777-6 Idioma : Inglés (eng) Palabras clave: Mathematics Coding theory Algorithms Bioinformatics Topology Combinatorics Statistics and Information Theory Algorithm Analysis Problem Complexity Computational Biology/Bioinformatics for Business/Economics/Mathematical Finance/Insurance Clasificación: 51 Matemáticas Resumen: The present volume is a collection of survey papers in the fields of entropy, search and complexity. They summarize the latest developments in their respective areas. More than half of the papers belong to search theory which lies on the borderline of mathematics and computer science, information theory and combinatorics, respectively. Search theory has variegated applications, among others in bioinformatics. Some of these papers also have links to linear statistics and communicational complexity. Further works survey the fundamentals of information theory and quantum source coding. The volume is recommended to experienced researchers as well as young scientists and students both in mathematics and computer science Nota de contenido: Two Colors and More -- Coding with Feedback and Searching with Lies -- Nonadaptive and Trivial Two-Stage Group Testing with Error-Correcting d e-Disjunct Inclusion Matrices -- Model Identification Using Search Linear Models and Search Designs -- Information Topologies with Applications -- Reinforced Random Walk -- Quantum Source Coding and Data Compression -- Information Theory at the Service of Science -- Analysis of Sorting Algorithms by Kolmogorov Complexity (A Survey) -- Recognition Problems in Combinatorial Search En línea: http://dx.doi.org/10.1007/978-3-540-32777-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34599 Entropy, Search, Complexity [documento electrónico] / SpringerLink (Online service) ; Csiszár, Imre ; Katona, Gyula O. H ; Tardos, Gábor ; Wiener, Gábor . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2007 . - VI, 262 p : online resource. - (Bolyai Society Mathematical Studies, ISSN 1217-4696; 16) .
ISBN : 978-3-540-32777-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Coding theory Algorithms Bioinformatics Topology Combinatorics Statistics and Information Theory Algorithm Analysis Problem Complexity Computational Biology/Bioinformatics for Business/Economics/Mathematical Finance/Insurance Clasificación: 51 Matemáticas Resumen: The present volume is a collection of survey papers in the fields of entropy, search and complexity. They summarize the latest developments in their respective areas. More than half of the papers belong to search theory which lies on the borderline of mathematics and computer science, information theory and combinatorics, respectively. Search theory has variegated applications, among others in bioinformatics. Some of these papers also have links to linear statistics and communicational complexity. Further works survey the fundamentals of information theory and quantum source coding. The volume is recommended to experienced researchers as well as young scientists and students both in mathematics and computer science Nota de contenido: Two Colors and More -- Coding with Feedback and Searching with Lies -- Nonadaptive and Trivial Two-Stage Group Testing with Error-Correcting d e-Disjunct Inclusion Matrices -- Model Identification Using Search Linear Models and Search Designs -- Information Topologies with Applications -- Reinforced Random Walk -- Quantum Source Coding and Data Compression -- Information Theory at the Service of Science -- Analysis of Sorting Algorithms by Kolmogorov Complexity (A Survey) -- Recognition Problems in Combinatorial Search En línea: http://dx.doi.org/10.1007/978-3-540-32777-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34599 Ejemplares
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Título : Error-Correcting Linear Codes : Classification by Isometry and Applications Tipo de documento: documento electrónico Autores: Anton Betten ; SpringerLink (Online service) ; Braun, Michael ; Fripertinger, Harald ; Kerber, Adalbert ; Kohnert, Axel ; Wassermann, Alfred Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2006 Colección: Algorithms and Computation in Mathematics, ISSN 1431-1550 num. 18 Número de páginas: XXIX, 798 p Il.: online resource ISBN/ISSN/DL: 978-3-540-31703-6 Idioma : Inglés (eng) Palabras clave: Mathematics Coding theory Algebra Algorithms Combinatorics and Information Theory Signal, Image Speech Processing Clasificación: 51 Matemáticas Resumen: This text offers a thorough introduction to the mathematical concepts behind the theory of error-correcting linear codes. Care is taken to introduce the necessary algebraic concepts, for instance the theory of finite fields, the polynomial rings over such fields and the ubiquitous concept of group actions that allows the classification of codes by isometry. The book provides in-depth coverage of important topics like cyclic codes and the coding theory used in compact disc players. The final four chapters cover advanced and algorithmic topics like the classification of linear codes by isometry, the enumeration of isometry classes, random generation of codes, the use of lattice basis reduction to compute minimum distances, the explicit construction of codes with given parameters, as well as the systematic evaluation of representatives of all isometry classes of codes. Up until now, these advanced topics have only been covered in research papers. The present book provides access to these results at a level which is suitable for graduate students of mathematics, computer science and engineering as well as for researchers Nota de contenido: Linear Codes -- Bounds and Modifications -- Finite Fields -- Cyclic Codes -- Mathematics and Audio Compact Discs -- Enumeration of Isometry Classes -- Solving Systems of Diophantine Linear Equations -- Linear Codes with a Prescribed Minimum Distance -- The General Case En línea: http://dx.doi.org/10.1007/3-540-31703-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34942 Error-Correcting Linear Codes : Classification by Isometry and Applications [documento electrónico] / Anton Betten ; SpringerLink (Online service) ; Braun, Michael ; Fripertinger, Harald ; Kerber, Adalbert ; Kohnert, Axel ; Wassermann, Alfred . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2006 . - XXIX, 798 p : online resource. - (Algorithms and Computation in Mathematics, ISSN 1431-1550; 18) .
ISBN : 978-3-540-31703-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Coding theory Algebra Algorithms Combinatorics and Information Theory Signal, Image Speech Processing Clasificación: 51 Matemáticas Resumen: This text offers a thorough introduction to the mathematical concepts behind the theory of error-correcting linear codes. Care is taken to introduce the necessary algebraic concepts, for instance the theory of finite fields, the polynomial rings over such fields and the ubiquitous concept of group actions that allows the classification of codes by isometry. The book provides in-depth coverage of important topics like cyclic codes and the coding theory used in compact disc players. The final four chapters cover advanced and algorithmic topics like the classification of linear codes by isometry, the enumeration of isometry classes, random generation of codes, the use of lattice basis reduction to compute minimum distances, the explicit construction of codes with given parameters, as well as the systematic evaluation of representatives of all isometry classes of codes. Up until now, these advanced topics have only been covered in research papers. The present book provides access to these results at a level which is suitable for graduate students of mathematics, computer science and engineering as well as for researchers Nota de contenido: Linear Codes -- Bounds and Modifications -- Finite Fields -- Cyclic Codes -- Mathematics and Audio Compact Discs -- Enumeration of Isometry Classes -- Solving Systems of Diophantine Linear Equations -- Linear Codes with a Prescribed Minimum Distance -- The General Case En línea: http://dx.doi.org/10.1007/3-540-31703-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34942 Ejemplares
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