# Lattices and Codes A Course Partially Based on Lectures by Friedrich Hirzebruch

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• "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"@en
• "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. ContentLattices and Codes -Theta Functions and Weight Enumerators - Even Unimodular Lattices - The Leech Lattice - Lattices over Integers of Number Fields and Self-Dual Codes. ReadershipGraduate Students in Mathematics and Computer ScienceMathematicians and Computer ScientistsAbout the AuthorProf. Dr. Wolfgang Ebeling, Institute of Algebraic Geometry, Leibniz Universität Hannover, Germany."@en
• "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: 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. We give a detailed introduction to these relations including recent results of G. van der Geer and F. Hirzebruch. Let us explain the history of this book. In [LPS82] J. S. Leon, V. Pless, and N. J. A. Sloane considered the Lee weight enumerators of self-dual codes over the prime field of characteristic 5. They wrote in the introduction to their paper: "The weight enumerator of anyone of the codes . . . is strongly constrained: it must be invariant under a three-dimensional representation of the icosahedral group. These invariants were already known to Felix Klein, and the consequences for coding theory were discovered by Gleason and Pierce (and independently by the third author) . . . (It is worth mentioning that precisely the same invariants have recently been studied by Hirzebruch in connection with cusps of the Hilbert modular surface associated with Q( J5)."@en
• "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 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."@en

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• "Electronic books"@en
• "Libros electrónicos"

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• "Lattices and Codes : A Course Partially Based on Lectures by Friedrich Hirzebruch"
• "Lattices and Codes A Course Partially Based on Lectures by Friedrich Hirzebruch"@en
• "Lattices and Codes A Course Partially Based on Lectures by Friedrich Hirzebruch"
• "Lattices and codes : A course partialley based on lectures by F.Hirzebruch"
• "Lattices and Codes a Course Partially Based on Lectures by F. Hirzebruch"@en
• "Lattices and Codes A Course Partially Based on Lectures by F. Hirzebruch"
• "Lattices and codes : a course partially based on lectures by F. Hirzebruch"
• "Lattices and codes : a course partially based on lectures by F. Hirzebruch"@en
• "Lattices and Codes: A Course Partially Based on Lectures by F. Hirzebruch"
• "Lattices and codes a course partially based on lectures by Friedrich Hirzebruch"@en
• "Lattices and codes a course partially based on lectures by Friedrich Hirzebruch"
• "Lattices and codes : a course partially based on lectures by Friedrich Hirzebruch"
• "Lattices and codes : a course partially based on lectures by Friedrich Hirzebruch"@en
• "Lattices and codes a course partially based on lectures by F. Hirzebruch"
• "Lattices and codes a course partially based on lectures by F. Hirzebruch"@en