Designs from Linear Codes

By: Cunsheng Ding

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eText | 24 August 2018

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This monograph aims to provide a well-rounded and detailed account of designs using linear codes. Most chapters of this monograph cover on the designs of linear codes. A few chapters deal with designs obtained from linear codes in other ways. Connections among ovals, hyperovals, maximal arcs, ovoids, linear codes and designs are also investigated. This book consists of both classical results on designs from linear codes and recent results yet published by others.

This monograph is intended to be a reference for postgraduates and researchers who work on combinatorics, or coding theory, or digital communications, or finite geometry.

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

Readership: Students and professionals working on combinatorics, or coding theory, or digital communications, or finite geometries.
Mechanics;Engineering Mechanics;Structural Engineering;Civil Engineering