| 书目名称 | Lattices and Codes |
| 副标题 | A Course Partially B |
| 编辑 | Wolfgang Ebeling |
| 视频video | |
| 概述 | Modern Aspects in the Design of Codes |
| 丛书名称 | Advanced Lectures in Mathematics |
| 图书封面 |  |
| 描述 | 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 |
| 出版日期 | Textbook 20022nd edition |
| 关键词 | Codierungstheorie; Even Unimodular Lattices; Leech Lattice; Number theory; algebra; coding theory |
| 版次 | 2 |
| doi | https://doi.org/10.1007/978-3-322-90014-2 |
| isbn_ebook | 978-3-322-90014-2Series ISSN 0932-7134 Series E-ISSN 2512-7039 |
| issn_series | 0932-7134 |
| copyright | Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden 2002 |
发表于 2025-3-21 16:41:03
