| 書(shū)目名稱(chēng) | Lattices and Codes |
| 副標(biāo)題 | A Course Partially B |
| 編輯 | Wolfgang Ebeling |
| 視頻video | http://file.papertrans.cn/582/581956/581956.mp4 |
| 叢書(shū)名稱(chēng) | Advanced Lectures in Mathematics |
| 圖書(shū)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 19941st edition |
| 關(guān)鍵詞 | Dimension; algebra; classification; code; coding; coding theory; design; error-correcting code; history; info |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-322-96879-1 |
| isbn_ebook | 978-3-322-96879-1Series ISSN 0932-7134 Series E-ISSN 2512-7039 |
| issn_series | 0932-7134 |
| copyright | Springer Fachmedien Wiesbaden 1994 |
|Archiver|手機(jī)版|小黑屋|
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