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This is the first monograph on codebooks and linear codes from difference sets and almost difference sets. It aims at providing a survey of constructions of difference sets and almost difference sets as well as an in-depth treatment of codebooks and linear codes from difference sets and almost difference sets. To be self-contained, this monograph covers necessary mathematical foundations and the basics of coding theory. It also contains tables of best BCH codes and best cyclic codes over GF(2) and GF(3) up to length 125 and 79, respectively. This repository of tables can be used to benchmark newly constructed cyclic codes.
This monograph is intended to be a reference for postgraduates and researchers who work on combinatorics, or coding theory, or digital communications.
Sample Chapter(s)
Chapter 1: Mathematical Foundations (244 KB)
Contents:
- Mathematical Foundations
- Linear Codes over Finite Fields
- Designs and Their Codes
- Difference Sets
- Almost Difference Sets
- Linear Codes of Difference Sets
- Linear Codes of Almost Difference Sets
- Codebooks from (Almost) Difference Sets
Readership: Students and professionals working on combinatorics, or coding theory, or digital communications.
