Designs from linear codes
"Since the publication of the first edition of this monograph, a generalisation of the Assmus-Mattson theorem for linear codes over finite fields has been developed, two 70-year breakthroughs and a considerable amount of other progress on t-designs from linear codes have been made. This second edition is a substantial revision and expansion of the first edition. Two new chapters and two new appendices have been added, and most chapters of the first edition have been revised. It provides a well-…
Read More ↓Title Statements
- Full title :Designs from linear codes / Cunsheng Ding, The Hong Kong University of Science and Technology, Hong Kong, Chunming Tang, China West Normal University, China.
Summary
"Since the publication of the first edition of this monograph, a generalisation of the Assmus-Mattson theorem for linear codes over finite fields has been developed, two 70-year breakthroughs and a considerable amount of other progress on t-designs from linear codes have been made. This second edition is a substantial revision and expansion of the first edition. Two new chapters and two new appendices have been added, and most chapters of the first edition have been revised. It provides a well-rounded and detailed account of t-designs from linear codes. Most chapters of this book cover the support designs of linear codes. A few chapters deal with designs obtained from linear codes in other ways. Connections among ovals, hyperovals, maximal arcs, ovoids, special functions, linear codes and designs are also investigated. This book consists of both classical and recent results on designs from linear codes. It is intended to be a reference for postgraduates and researchers who work on combinatorics, or coding theory, or digital communications, or finite geometry. It can also be used as a textbook for postgraduates in these subject areas"--
Read More ↓Edition Statements
- Publication Date:©2022
- Edition:Second edition
Publication Statements
- Publisher(s):World Scientific Publishing Co Pte Ltd
- Place of Publication:Singapore
- Language:eng
- Publication Date:©2022
The Physical Object
- Description:1 online resource (xvii, 521 pages) : : illustrations
Edition Identifiers
- ISBN:9789811251337, 9811251339
- oclc:on1292972917
- LC Classification:QA268
- Dewey Decimal:003/.54
Table of Contents
Mathematical foundations -- Linear codes over finite fields -- Cyclic codes over finite fields -- Designs and codes -- Designs of binary Reed-Muller codes -- Affine invariant codes and their designs -- Weights in some BCH codes over GF(q) -- Designs from four types of linear codes -- Designs from primitive BCH codes -- Designs from codes with regularity -- Designs from QR and self-dual codes -- Designs from arc and MDS codes -- Designs from ovoid codes -- Quasi-symmetric designs from bent codes -- Almost MDS codes and their designs -- Beyond the Assmus-Mattson theorem.
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