Applications of Abstract Algebra with Maple

Table of contents

Finite Fields
Finite Field Computations
Finite Fields Using Maple
Block Designs
Block Designs
Hadamard Matrices
Hadamard Matrices Using Maple
Difference Sets
Difference Sets Using Maple
Error Correcting Codes
Introduction
Hadamard Codes
Reed-Muller Codes
Reed-Muller Codes Using Maple
Linear Codes
Hamming Codes With Maple
BCH Codes
Codeword Generation
Codeword Correction
Reed-Solomon Codes
The Euclidean Algorithm
Reed-Solomon Codes Over
The Fundamental Equation
Computing the Polynomials
Binary Reed-Solomon Codes and Burst Error Correction
Reed-Solomon Codes with Maple
Codeword Generation
Codeword Correction
Application of Reed-Solomon Codes: Voyager
Algebraic Cryptography
Introduction
Hill System
Basic Description
Cryptanalysis of the Hill System
Variable Matrix Substitution
Implementing the Hill System with Maple
Message encipherment
Message Decipherment
The RSA Cryptosystem
Introduction
Zn and
Implementing the RSA Cryptosystem
Basic Theory
Exponentiating Large Numbers with Maple
The Public Key
Primality Testing
Description of Basic Methods
Primality Algorithms Implemented Using Maple
Factorization
Basic Techniques
Pollard Rho
Factoring Algorithms Implemented With Maple
Built-in Maple Commands for Primality Testing and Factoring
Implementing the RSA with Maple
The Polya Enumeration Theorem
Group Actions
The Burnside Theorem
The Cycle Index
The Pattern Inventory
Polya Enumeration Formula
Computing the Pattern Inventory with Maple
Switching Functions
Switching Functions with Maple
Non-directed Graphs of Order n
The Cycle Index for Sn
Graphs of Orderne
Appendix