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Synopsis
The purpose of coding theory is the design of efficient systems for the transmission of information. The mathematical treatment leads to certain finite structures - the error-correcting codes. Surprisingly, problems which are interesting for the design of codes turn out to be closely related to problems studied partly earlier and independently in pure mathematics. This book is about an example of such a connection. It is about the relation between codes and lattices. Lattices are studied in number theory and in the geometry of numbers. Many problems about codes have their counterpart in problems about lattices and sphere packings. The book starts with the basic definitions and examples of lattices and codes. A central theme is a fundamental correspondence between binary linear codes and certain integral lattices. The theta function of a lattice is introduced and it is shown that it is a modular form. Several applications of the theory of modeular forms to weight enumerators of codes are discussed. The classification of even unimodular lattices up to dimension 24 is studied using theta functions with spherical coefficients. Special attention is devoted to the Leech lattice, its constructions and the sphere covering determined by it. Finally, the book contains a detailed account on recent results of G. van der Geer and F. Hirzebruch concerning a generalization of some of the relations studied earlier in the book to self-dual codes over certain finite fields with more than two elements and lattices over the integers of certain algebraic fields. The book can serve as a text for a course. It should also be of use for students and mathematicians working in number theory, geometry or coding theory.
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Présentation de l'éditeur
The purpose of coding theory is the design of efficient systems for the transmission of information. The mathematical treatment leads to certain finite structures: the error-correcting codes. Surprisingly problems which are interesting for the design of codes turn out to be closely related to problems studied partly earlier and independently in pure mathematics. In this book, examples of such connections are presented. The relation between lattices studied in number theory and geometry and error-correcting codes is discussed. The book provides at the same time an introduction to the theory of integral lattices and modular forms and to coding theory. In the 3rd edition, again numerous corrections and improvements have been made and the text has been updated.
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Lattices and codes a course partially based on lectures. Advanced lectures in mathematics Vieweg.
Edité par
Braunschweig, Vieweg [1994]., 1994
ISBN 10 : 3528064978
ISBN 13 : 9783528064976
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Softcover
Vendeur : Antiquariat Bookfarm, Löbnitz, Allemagne
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Softcover. Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ancien Exemplaire de bibliothèque avec signature et cachet. BON état, quelques traces d'usure. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. 11 EBE 9783528064976 Sprache: Englisch Gewicht in Gramm: 550. N° de réf. du vendeur 2504044
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Lattices and Codes A Course Partially Based on Lectures by F. Hirzebruch
Edité par
Braunschweig ; Wiesbaden : Vieweg, 1994
ISBN 10 : 3528064978
ISBN 13 : 9783528064976
Ancien ou d'occasion
23 x 16,5 cm
Vendeur : avelibro OHG, Dinkelscherben, Allemagne
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23 x 16,5 cm. Etat : Gut. Advanced Lectures in Mathematics. XII, 178 Pages ; With Figures Original Broschur mit Bibliotheksschild auf Vorderdeckel. Innen mit Bibliotheksstempeln, sehr sauberes Exemplar. Englische Sprache. - Original Paperback with Library label on front cover. Inside with Library stamps, in very good condition. English Language B15-03-02D|S99 Altersfreigabe FSK ab 0 Jahre Sprache: Englisch Gewicht in Gramm: 354. N° de réf. du vendeur 62820
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Lattices and Codes: A Course Partially Based on Lectures by F. Hirzebruch (Advanced Lectures in Mathematics) Ebeling, Wolfgang
Edité par
Vieweg, 1994
ISBN 10 : 3528064978
ISBN 13 : 9783528064976
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Couverture souple
Vendeur : BUCHSERVICE / ANTIQUARIAT Lars Lutzer, Wahlstedt, Allemagne
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Etat : gut. Rechnung mit MwSt - Versand aus Deutschland pages. N° de réf. du vendeur 8O-29K1-F63L
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Lattices and Codes: A Course Partially Based on Lectures by F. Hirzebruch (Advanced Lectures in Mathematics) Ebeling, Wolfgang
Edité par
Vieweg, 1994
ISBN 10 : 3528064978
ISBN 13 : 9783528064976
Ancien ou d'occasion
Couverture souple
Vendeur : BUCHSERVICE / ANTIQUARIAT Lars Lutzer, Wahlstedt, Allemagne
Évaluation du vendeur 5 sur 5 étoiles
Etat : gut. Rechnung mit MwSt - Versand aus Deutschland pages. N° de réf. du vendeur PZ-CPBZ-7ANZ
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Lattices and Codes: A Course Partially Based on Lectures by F. Hirzebruch (Advanced lectures in mathematics) von Wolfgang Ebeling (Autor), Friedrich Hirzebruch Lattices and Codes - Theta Functions and Weight Enumerators - Even Unimodular Lattices - The Leech Lattice - Lattices over Integers of Number Fields and Self-Dual Codes Über den Autor Prof. Dr. Wolfgang Ebeling, Department of Mathematics, Universität Hannover, Germany. This is the second revised edition of a textbook on coding theory. The purpose of coding theory is the design of efficient systems for the transmission of information. The mathematical treatment leads to certain finite structuresthe error-correcting codes. Surprisingly problems which are interesting for the design of codes turn out to be closely related to problems studied partly earlier and independently in pure mathematics. In this book, examples of such connections are presented. The relation between lattices studied in number theory and geometry and error-corr
Edité par
Vieweg+Teubner Verlag Auflage: 1994 (1. Januar 1994), 1994
ISBN 10 : 3528064978
ISBN 13 : 9783528064976
Ancien ou d'occasion
Softcover
Vendeur : BUCHSERVICE / ANTIQUARIAT Lars Lutzer, Wahlstedt, Allemagne
Évaluation du vendeur 5 sur 5 étoiles
Softcover. Etat : gut. Auflage: 1994 (1. Januar 1994). Lattices and CodesA Course Partially Based on Lectures by F. Hirzebruch (Advanced lectures in mathematics) Wolfgang Ebeling Friedrich Hirzebruch Code Barcode Codierung Kode Barcode Gewinn Department of Mathematics Universität Hannover Even Unimodular Lattices and Codes - Theta Functions and Weight Enumerators - Even Unimodular Lattices - The Leech Lattice - Lattices over Integers of Number Fields and Self-Dual Codes Über den Autor Prof. Dr. Wolfgang Ebeling, Department of Mathematics, Universität Hannover, Germany. This is the second revised edition of a textbook on coding theory. The purpose of coding theory is the design of efficient systems for the transmission of information. The mathematical treatment leads to certain finite structuresthe error-correcting codes. Surprisingly problems which are interesting for the design of codes turn out to be closely related to problems studied partly earlier and independently in pure mathematics. In this book, examples of such connections are presented. The relation between lattices studied in number theory and geometry and error-correcting codes is discussed. The book provides at the same time an introduction to the theory of integral lattices and modular forms and to coding theory. Beschreibung The purpose of coding theory is the design of efficient systems for the transmission of information. The mathematical treatment leads to certain finite structuresthe error-correcting codes. Surprisingly problems which are interesting for the design of codes turn out to be closely related to problems studied partly earlier and independently in pure mathematics. In this book, examples of such connections are presented. The relation between lattices studied in number theory and geometry and error-correcting codes is discussed. The book provides at the same time an introduction to the theory of integral lattices and modular forms and to coding theory. In the 2nd edition numerous corrections have been made. More basic material has been included to make the text even more self-contained. A new section on the automorphism group of the Leech lattice has been added. Some hints to new results have been incorporated. Finally, several new exercises have been added. From the contents - Lattices and Codes - Theta Functions and Weight Enumerators - Even Unimodular Lattices - The Leech Lattice - Lattices over Integers of Number Fields and Self-Dual Codes In englischer Sprache. 178 pages. 24,4 x 17 x 1,7 cm. N° de réf. du vendeur BN12461
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