Restricted congruences in computing:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Boca Raton ; London ; New York
CRC Press
2021
|
| Ausgabe: | First edition |
| Links: | https://ebookcentral.proquest.com/lib/munchentech/detail.action?docID=6303885 |
| Beschreibung: | Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Contents -- Preface -- Chapter 1: Introduction -- 1.1 MOTIVATION -- 1.2 OVERVIEW OF THE BOOK -- Chapter 2: The Restricted Congruences Toolbox -- 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, AND CHARACTERS -- Chapter 3: The GCD-Restricted Linear Congruences -- 3.1 INTRODUCTION -- 3.2 Linear Congruences with (xi, n) = ti (1 ≤ i ≤ k) -- 3.3 AN EQUIVALENT FORM OF THEOREM 3.2.4 -- 3.4 SOME PROBLEMS -- Chapter 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 -- Chapter 5: Applications in String Theory and Quantum Field Theory -- 5.1 INTRODUCTION -- 5.2 COUNTING SURFACE-KERNEL EPIMORPHISMS FROM -- 5.3 A PROBLEM -- Chapter 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 -- 6.4.1 Ordered Partitions Acted upon by Cyclic Permutations -- 6.4.2 Permutations with Given Cycle Structure and Descent Set -- 6.4.3 Fixed-Density Necklaces and Lyndon Words -- 6.4.4 Necklace Polynomial -- 6.4.5 Quasi-Necklace Polynomial -- 6.5 A PROBLEM -- Chapter 7: Alldiff Congruences Meet VT Codes -- 7.1 INTRODUCTION -- 7.2 MAIN RESULTS -- Chapter 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 -- Chapter 9: Applications in Parallel Computing, AI, etc. -- 9.1 APPLICATION IN PARALLEL COMPUTING -- 9.2 APPLICATION IN ARTIFICIAL INTELLIGENCE AND COMPUTATIONAL BIOLOGY -- 9.3 APPLICATION IN THE SUBSET-SUM PROBLEM -- Chapter 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 |
| Umfang: | 1 Online-Ressource (xi, 145 Seiten) |
| ISBN: | 9781000173130 9781003047179 |
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| 500 | |a Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Contents -- Preface -- Chapter 1: Introduction -- 1.1 MOTIVATION -- 1.2 OVERVIEW OF THE BOOK -- Chapter 2: The Restricted Congruences Toolbox -- 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, AND CHARACTERS -- Chapter 3: The GCD-Restricted Linear Congruences -- 3.1 INTRODUCTION -- 3.2 Linear Congruences with (xi, n) = ti (1 ≤ i ≤ k) -- 3.3 AN EQUIVALENT FORM OF THEOREM 3.2.4 -- 3.4 SOME PROBLEMS -- Chapter 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 -- Chapter 5: Applications in String Theory and Quantum Field Theory -- 5.1 INTRODUCTION -- 5.2 COUNTING SURFACE-KERNEL EPIMORPHISMS FROM -- 5.3 A PROBLEM -- Chapter 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 -- 6.4.1 Ordered Partitions Acted upon by Cyclic Permutations -- 6.4.2 Permutations with Given Cycle Structure and Descent Set -- 6.4.3 Fixed-Density Necklaces and Lyndon Words -- 6.4.4 Necklace Polynomial -- 6.4.5 Quasi-Necklace Polynomial -- 6.5 A PROBLEM -- Chapter 7: Alldiff Congruences Meet VT Codes -- 7.1 INTRODUCTION -- 7.2 MAIN RESULTS -- Chapter 8: Binary Linear Congruence Code -- 8.1 INTRODUCTION. | ||
| 500 | |a 8.2 WEIGHT ENUMERATOR OF THE BINARY LINEAR CONGRUENCE CODE -- 8.3 WEIGHT ENUMERATORS OF THE AFOREMENTIONED CODES -- Chapter 9: Applications in Parallel Computing, AI, etc. -- 9.1 APPLICATION IN PARALLEL COMPUTING -- 9.2 APPLICATION IN ARTIFICIAL INTELLIGENCE AND COMPUTATIONAL BIOLOGY -- 9.3 APPLICATION IN THE SUBSET-SUM PROBLEM -- Chapter 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 | ||
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Datensatz im Suchindex
| DE-BY-TUM_katkey | 2509269 |
|---|---|
| _version_ | 1821936103741980672 |
| any_adam_object | |
| author | Bibak, Khodakhast |
| author_GND | (DE-588)1258738694 |
| author_facet | Bibak, Khodakhast |
| author_role | aut |
| author_sort | Bibak, Khodakhast |
| author_variant | k b kb |
| building | Verbundindex |
| bvnumber | BV047017350 |
| classification_tum | DAT 500 |
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| ctrlnum | (ZDB-30-PQE)EBC6303885 (OCoLC)1224015947 (DE-599)BVBBV047017350 |
| dewey-full | 512.72 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.72 |
| dewey-search | 512.72 |
| dewey-sort | 3512.72 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| edition | First edition |
| format | Electronic eBook |
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| id | DE-604.BV047017350 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T19:07:25Z |
| institution | BVB |
| isbn | 9781000173130 9781003047179 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032424885 |
| oclc_num | 1224015947 |
| open_access_boolean | |
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| owner_facet | DE-91 DE-BY-TUM |
| physical | 1 Online-Ressource (xi, 145 Seiten) |
| psigel | ZDB-30-PQE ZDB-30-PQE TUM_PDA_PQE_Kauf |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | CRC Press |
| record_format | marc |
| spellingShingle | Bibak, Khodakhast Restricted congruences in computing |
| title | Restricted congruences in computing |
| title_auth | Restricted congruences in computing |
| title_exact_search | Restricted congruences in computing |
| title_full | Restricted congruences in computing Khodakhast Bibak |
| title_fullStr | Restricted congruences in computing Khodakhast Bibak |
| title_full_unstemmed | Restricted congruences in computing Khodakhast Bibak |
| title_short | Restricted congruences in computing |
| title_sort | restricted congruences in computing |
| work_keys_str_mv | AT bibakkhodakhast restrictedcongruencesincomputing |