Designs From Linear Codes (Second Edition)

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.
Contents:

• Preface

• Preface to the First Edition

• 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 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

• Appendices:

  • Sporadic Designs from Linear Codes
  • Designs from Binary Codes with Regularities
  • Exercises on Mathematical Foundations

• Bibliography

• Notation and Symbols

• Index

Readership: Students and professionals working on combinatorics, or coding theory, or digital communications, or finite geometries.
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