Restricted Congruences in Computing
portes grátis
Restricted Congruences in Computing
Bibak, Khodakhast
Taylor & Francis Ltd
09/2020
145
Dura
Inglês
9780367496036
15 a 20 dias
450
Descrição não disponível.
Preface
Dedication
1 Introduction
1.1 Motivation
1.2 Overview of the book
2 The Restricted Congruences Toolbox 6
2.1 Ramanujan sums
2.2 Some useful identities
2.3 The discrete Fourier transform
2.4 Universal hashing and its variants
2.5 Multilinear Modular Hashing
2.6 Fuchsian groups and Harvey's theorem
2.7 Counting epimorphisms via homomorphisms
2.8 Generating functions for graph enumeration
2.9 Deletion correcting codes
2.10 Weight enumerator of a code
2.11 Gaussian integers, spectral graph theory, characters
3 The GCD-Restricted Linear Congruences
3.1 Introduction
3.2 Linear congruences with
3.3 An equivalent form of Theorem 3.2.4
3.4 Some problems
4 Applications in Universal Hashing and Authentication with Secrecy
4.1 Introduction
4.2 Generalized Multilinear Modular Hashing
4.3 GRDH
4.4 Applications to authentication with secrecy
4.5 Discussion
5 Applications in String Theory and Quantum Field Theory
5.1 Introduction
5.2 Counting surface-kernel epimorphisms from ? to Zn
5.3 A problem
6 Alldiff Congruences, Graph Theoretic Method, and Beyond
6.1 Introduction
6.2 Graph theoretic method
6.3 Unweighted alldiff congruences
6.4 More applications and connections
6.5 A problem
7 Alldiff Congruences Meet VT Codes
7.1 Introduction
7.2 Main results
8 Binary Linear Congruence Code
8.1 Introduction
8.2 Weight enumerator of the Binary Linear Congruence Code
8.3 Weight enumerators of the aforementioned codes
9 Applications in Parallel Computing, AI, etc
9.1 Application in parallel computing
9.2 Application in arti?ficial intelligence and computational biology
9.3 Application in the Subset-Sum Problem
10 Quadratic Congruences, Ramanujan Graphs, and the Golomb-Welch Conjecture
10.1 Introduction
10.2 Quadratic congruences
10.3 Proof of the conjecture
10.4 A problem
Bibliography
Index
Dedication
1 Introduction
1.1 Motivation
1.2 Overview of the book
2 The Restricted Congruences Toolbox 6
2.1 Ramanujan sums
2.2 Some useful identities
2.3 The discrete Fourier transform
2.4 Universal hashing and its variants
2.5 Multilinear Modular Hashing
2.6 Fuchsian groups and Harvey's theorem
2.7 Counting epimorphisms via homomorphisms
2.8 Generating functions for graph enumeration
2.9 Deletion correcting codes
2.10 Weight enumerator of a code
2.11 Gaussian integers, spectral graph theory, characters
3 The GCD-Restricted Linear Congruences
3.1 Introduction
3.2 Linear congruences with
3.3 An equivalent form of Theorem 3.2.4
3.4 Some problems
4 Applications in Universal Hashing and Authentication with Secrecy
4.1 Introduction
4.2 Generalized Multilinear Modular Hashing
4.3 GRDH
4.4 Applications to authentication with secrecy
4.5 Discussion
5 Applications in String Theory and Quantum Field Theory
5.1 Introduction
5.2 Counting surface-kernel epimorphisms from ? to Zn
5.3 A problem
6 Alldiff Congruences, Graph Theoretic Method, and Beyond
6.1 Introduction
6.2 Graph theoretic method
6.3 Unweighted alldiff congruences
6.4 More applications and connections
6.5 A problem
7 Alldiff Congruences Meet VT Codes
7.1 Introduction
7.2 Main results
8 Binary Linear Congruence Code
8.1 Introduction
8.2 Weight enumerator of the Binary Linear Congruence Code
8.3 Weight enumerators of the aforementioned codes
9 Applications in Parallel Computing, AI, etc
9.1 Application in parallel computing
9.2 Application in arti?ficial intelligence and computational biology
9.3 Application in the Subset-Sum Problem
10 Quadratic Congruences, Ramanujan Graphs, and the Golomb-Welch Conjecture
10.1 Introduction
10.2 Quadratic congruences
10.3 Proof of the conjecture
10.4 A problem
Bibliography
Index
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
Linear Congruence;coding theory;Cayley Graphs;information security;Ramanujan Sum;restricted congruence;Ramanujan Graph;quantum field theory;Weight Enumerator;parallel computing;Subset Sum Problem;Explicit Formula;Prime Divisor;DFT;Compact Riemann Surfaces;Edit Distance;Ribbon Graphs;Hash Functions;SVT;Finite Abelian Group;Hamming Weight;Universal Hash;Spectral Graph Theory;QFT;Positive Divisors;Levenshtein Distance;Binary Solutions;String Theory;Smallest Prime Divisor;Fuchsian Group
Preface
Dedication
1 Introduction
1.1 Motivation
1.2 Overview of the book
2 The Restricted Congruences Toolbox 6
2.1 Ramanujan sums
2.2 Some useful identities
2.3 The discrete Fourier transform
2.4 Universal hashing and its variants
2.5 Multilinear Modular Hashing
2.6 Fuchsian groups and Harvey's theorem
2.7 Counting epimorphisms via homomorphisms
2.8 Generating functions for graph enumeration
2.9 Deletion correcting codes
2.10 Weight enumerator of a code
2.11 Gaussian integers, spectral graph theory, characters
3 The GCD-Restricted Linear Congruences
3.1 Introduction
3.2 Linear congruences with
3.3 An equivalent form of Theorem 3.2.4
3.4 Some problems
4 Applications in Universal Hashing and Authentication with Secrecy
4.1 Introduction
4.2 Generalized Multilinear Modular Hashing
4.3 GRDH
4.4 Applications to authentication with secrecy
4.5 Discussion
5 Applications in String Theory and Quantum Field Theory
5.1 Introduction
5.2 Counting surface-kernel epimorphisms from ? to Zn
5.3 A problem
6 Alldiff Congruences, Graph Theoretic Method, and Beyond
6.1 Introduction
6.2 Graph theoretic method
6.3 Unweighted alldiff congruences
6.4 More applications and connections
6.5 A problem
7 Alldiff Congruences Meet VT Codes
7.1 Introduction
7.2 Main results
8 Binary Linear Congruence Code
8.1 Introduction
8.2 Weight enumerator of the Binary Linear Congruence Code
8.3 Weight enumerators of the aforementioned codes
9 Applications in Parallel Computing, AI, etc
9.1 Application in parallel computing
9.2 Application in arti?ficial intelligence and computational biology
9.3 Application in the Subset-Sum Problem
10 Quadratic Congruences, Ramanujan Graphs, and the Golomb-Welch Conjecture
10.1 Introduction
10.2 Quadratic congruences
10.3 Proof of the conjecture
10.4 A problem
Bibliography
Index
Dedication
1 Introduction
1.1 Motivation
1.2 Overview of the book
2 The Restricted Congruences Toolbox 6
2.1 Ramanujan sums
2.2 Some useful identities
2.3 The discrete Fourier transform
2.4 Universal hashing and its variants
2.5 Multilinear Modular Hashing
2.6 Fuchsian groups and Harvey's theorem
2.7 Counting epimorphisms via homomorphisms
2.8 Generating functions for graph enumeration
2.9 Deletion correcting codes
2.10 Weight enumerator of a code
2.11 Gaussian integers, spectral graph theory, characters
3 The GCD-Restricted Linear Congruences
3.1 Introduction
3.2 Linear congruences with
3.3 An equivalent form of Theorem 3.2.4
3.4 Some problems
4 Applications in Universal Hashing and Authentication with Secrecy
4.1 Introduction
4.2 Generalized Multilinear Modular Hashing
4.3 GRDH
4.4 Applications to authentication with secrecy
4.5 Discussion
5 Applications in String Theory and Quantum Field Theory
5.1 Introduction
5.2 Counting surface-kernel epimorphisms from ? to Zn
5.3 A problem
6 Alldiff Congruences, Graph Theoretic Method, and Beyond
6.1 Introduction
6.2 Graph theoretic method
6.3 Unweighted alldiff congruences
6.4 More applications and connections
6.5 A problem
7 Alldiff Congruences Meet VT Codes
7.1 Introduction
7.2 Main results
8 Binary Linear Congruence Code
8.1 Introduction
8.2 Weight enumerator of the Binary Linear Congruence Code
8.3 Weight enumerators of the aforementioned codes
9 Applications in Parallel Computing, AI, etc
9.1 Application in parallel computing
9.2 Application in arti?ficial intelligence and computational biology
9.3 Application in the Subset-Sum Problem
10 Quadratic Congruences, Ramanujan Graphs, and the Golomb-Welch Conjecture
10.1 Introduction
10.2 Quadratic congruences
10.3 Proof of the conjecture
10.4 A problem
Bibliography
Index
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
Linear Congruence;coding theory;Cayley Graphs;information security;Ramanujan Sum;restricted congruence;Ramanujan Graph;quantum field theory;Weight Enumerator;parallel computing;Subset Sum Problem;Explicit Formula;Prime Divisor;DFT;Compact Riemann Surfaces;Edit Distance;Ribbon Graphs;Hash Functions;SVT;Finite Abelian Group;Hamming Weight;Universal Hash;Spectral Graph Theory;QFT;Positive Divisors;Levenshtein Distance;Binary Solutions;String Theory;Smallest Prime Divisor;Fuchsian Group
