{"product_id":"hadamard-matrices-constructions-using-number-theory-and-linear-algebra-hardback-9781119520245","title":"Hadamard Matrices; Constructions using Number Theory and Linear Algebra (Hardback) 9781119520245","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eHadamard Matrices\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eConstructions using Number Theory and Linear Algebra\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eJennifer Seberry (Author), Mieko Yamada (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781119520245, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 25 September 2020\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e352 pages\u003cbr\u003e1 x 1 x 1 cm, 0.454 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\u003cb\u003eUp-to-date resource on Hadamard matrices\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eHadamard Matrices: Constructions using Number Theory and Algebra \u003c\/i\u003eprovides students with a discussion of the basic definitions used for Hadamard Matrices as well as more advanced topics in the subject, including:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eGauss sums, Jacobi sums and relative Gauss sums\u003c\/li\u003e \u003cli\u003eCyclotomic numbers\u003c\/li\u003e \u003cli\u003ePlug-in matrices, arrays, sequences and M-structure\u003c\/li\u003e \u003cli\u003eGalois rings and Menon Hadamard differences sets\u003c\/li\u003e \u003cli\u003ePaley difference sets and Paley type partial difference sets\u003c\/li\u003e \u003cli\u003eSymmetric Hadamard matrices, skew Hadamard matrices and amicable Hadamard matrices\u003c\/li\u003e \u003cli\u003eA discussion of asymptotic existence of Hadamard matrices\u003c\/li\u003e \u003cli\u003eMaximal determinant matrices, embeddability of Hadamard matrices and growth problem for Hadamard matrices\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThe book can be used as a textbook for graduate courses in combinatorics, or as a reference for researchers studying Hadamard matrices.\u003c\/p\u003e \u003cp\u003eUtilized in the fields of signal processing and design experiments, Hadamard matrices have been used for 150 years, and remain practical today. \u003ci\u003eHadamard Matrices \u003c\/i\u003ecombines a thorough discussion of the basic concepts underlying the subject matter with more advanced applications that will be of interest to experts in the area.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eList of Tables xiii\u003cbr\u003eList of Figures xv\u003cbr\u003ePreface xvii\u003cbr\u003eAcknowledgments xix\u003cbr\u003eAcronyms xxi\u003cbr\u003eIntroduction xxiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Basic Definitions 1\u003c\/b\u003e\u003cbr\u003e1.1 Notations 1\u003cbr\u003e1.2 Finite Fields 1\u003cbr\u003e1.3 Group Rings and Their Characters 8\u003cbr\u003e1.4 Type 1 and Type 2 Matrices 9\u003cbr\u003e1.5 Hadamard Matrices 14\u003cbr\u003e1.6 Paley Core Matrices 20\u003cbr\u003e1.7 Amicable Hadamard Matrices 22\u003cbr\u003e1.8 The Additive Property and Four Plug-In Matrices 26\u003cbr\u003e1.9 Difference Sets, Supplementary Difference Sets, and Partial Difference Sets 28\u003cbr\u003e1.10 Sequences and Autocorrelation Function 33\u003cbr\u003e1.11 Excess 37\u003cbr\u003e1.12 Balanced Incomplete Block Designs 39\u003cbr\u003e1.13 Hadamard Matrices and SBIBDs 41\u003cbr\u003e1.14 Cyclotomic Numbers 41\u003cbr\u003e1.15 Orthogonal Designs and Weighing Matrices 46\u003cbr\u003e1.16 T-matrices, T-sequences, and Turyn Sequences 47\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Gauss Sums, Jacobi Sums, and Relative Gauss Sums 49\u003c\/b\u003e\u003cbr\u003e2.1 Notations 49\u003cbr\u003e2.2 Gauss Sums 49\u003cbr\u003e2.3 Jacobi Sums 51\u003cbr\u003e2.4 Cyclotomic Numbers and Jacobi Sums 60\u003cbr\u003e2.5 Relative Gauss Sums 69\u003cbr\u003e2.6 Prime Ideal Factorization of Gauss Sums 72\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Plug-In Matrices 77\u003c\/b\u003e\u003cbr\u003e3.1 Notations 77\u003cbr\u003e3.2 Williamson Type and Williamson Matrices 77\u003cbr\u003e3.3 Plug-In Matrices 82\u003cbr\u003e3.4 Eight Plug-In Matrices 84\u003cbr\u003e3.5 More T-sequences and T-matrices 85\u003cbr\u003e3.6 Construction of T-matrices of Order 6m + 1 87\u003cbr\u003e3.7 Williamson Hadamard Matrices and Paley Type II Hadamard Matrices 90\u003cbr\u003e3.8 Hadamard Matrices of Generalized Quaternion Type 97\u003cbr\u003e3.9 Supplementary Difference Sets and Williamson Matrices 100\u003cbr\u003e3.10 Relative Difference Sets and Williamson-Type Matrices over Abelian Groups 110\u003cbr\u003e3.11 Computer Construction of Williamson Matrices 112\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Arrays: Matrices to Plug-Into 115\u003c\/b\u003e\u003cbr\u003e4.1 Notations 115\u003cbr\u003e4.2 Orthogonal Designs 115\u003cbr\u003e4.3 Welch and Ono–Sawade–Yamamoto Arrays 121\u003cbr\u003e4.4 Regular Representation of a Group and BHW(G) 122\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Sequences 125\u003c\/b\u003e\u003cbr\u003e5.1 Notations 125\u003cbr\u003e5.2 PAF and NPAF 125\u003cbr\u003e5.3 Suitable Single Sequences 126\u003cbr\u003e5.4 Suitable Pairs of NPAF Sequences: Golay Sequences 131\u003cbr\u003e5.5 Current Results for Golay Pairs 131\u003cbr\u003e5.6 Recent Results for Periodic Golay Pairs 133\u003cbr\u003e5.7 More on Four Complementary Sequences 133\u003cbr\u003e5.8 6-Turyn-Type Sequences 136\u003cbr\u003e5.9 Base Sequences 137\u003cbr\u003e5.10 Yang-Sequences 137\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 M-structures 145\u003c\/b\u003e\u003cbr\u003e6.1 Notations 145\u003cbr\u003e6.2 The Strong Kronecker Product 145\u003cbr\u003e6.3 Reducing the Powers of 2 147\u003cbr\u003e6.4 Multiplication Theorems Using M-structures 149\u003cbr\u003e6.5 Miyamoto's Theorem and Corollaries via M-structures 151\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Menon Hadamard Difference Sets and Regular Hadamard Matrices 159\u003c\/b\u003e\u003cbr\u003e7.1 Notations 159\u003cbr\u003e7.2 Menon Hadamard Difference Sets and Exponent Bound 159\u003cbr\u003e7.3 Menon Hadamard Difference Sets and Regular Hadamard Matrices 160\u003cbr\u003e7.4 The Constructions from Cyclotomy 161\u003cbr\u003e7.5 The Constructions Using Projective Sets 165x Contents\u003cbr\u003e7.6 The Construction Based on Galois Rings 170\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Paley Hadamard Difference Sets and Paley Type Partial Difference Sets 175\u003c\/b\u003e\u003cbr\u003e8.1 Notations 175\u003cbr\u003e8.2 Paley Core Matrices and Gauss Sums 175\u003cbr\u003e8.3 Paley Hadamard Difference Sets 178\u003cbr\u003e8.4 Paley Type Partial Difference Set 182\u003cbr\u003e8.5 The Construction of Paley Type PDS from a Covering Extended Building Set 183\u003cbr\u003e8.6 Constructing Paley Hadamard Difference Sets 191\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Skew Hadamard, Amicable, and Symmetric Matrices 193\u003c\/b\u003e\u003cbr\u003e9.1 Notations 193\u003cbr\u003e9.2 Introduction 193\u003cbr\u003e9.3 Skew Hadamard Matrices 193\u003cbr\u003e9.4 Constructions for Skew Hadamard Matrices 195\u003cbr\u003e9.5 Szekeres Difference Sets 200\u003cbr\u003e9.6 Amicable Hadamard Matrices 204\u003cbr\u003e9.7 Amicable Cores 207\u003cbr\u003e9.8 Construction for Amicable Hadamard Matrices of Order 2t 208\u003cbr\u003e9.9 Construction of Amicable Hadamard Matrices Using Cores 209\u003cbr\u003e9.10 Symmetric Hadamard Matrices 211\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Skew Hadamard Difference Sets 215\u003c\/b\u003e\u003cbr\u003e10.1 Notations 215\u003cbr\u003e10.2 Skew Hadamard Difference Sets 215\u003cbr\u003e10.3 The Construction by Planar Functions Over a Finite Field 215\u003cbr\u003e10.4 The Construction by Using Index 2 Gauss Sums 218\u003cbr\u003e10.5 The Construction by Using Normalized Relative Gauss Sums 226\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Asymptotic Existence of Hadamard Matrices 233\u003c\/b\u003e\u003cbr\u003e11.1 Notations 233\u003cbr\u003e11.2 Introduction 233\u003cbr\u003e11.3 Seberry's Theorem 233\u003cbr\u003e11.4 Craigen's Theorem 234\u003cbr\u003e11.5 More Asymptotic Theorems 243\u003cbr\u003e11.6 Skew Hadamard and Regular Hadamard 243\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 More on Maximal Determinant Matrices 245\u003c\/b\u003e\u003cbr\u003e12.1 Notations 245\u003cbr\u003e12.2 E-Equivalence: The Smith Normal Form 245\u003cbr\u003e12.3 E-Equivalence: The Number of Small Invariants 247\u003cbr\u003e12.4 E-Equivalence: Skew Hadamard and Symmetric Conference Matrices 250\u003cbr\u003e12.5 Smith Normal Form for Powers of 2 252\u003cbr\u003e12.6 Matrices with Elements (1, −1) and Maximal Determinant 253\u003cbr\u003e12.7 D-Optimal Matrices Embedded in Hadamard Matrices 254\u003cbr\u003e12.8 Embedding of Hadamard Matrices within Hadamard Matrices 257\u003cbr\u003e12.9 Embedding Properties Via Minors 257\u003cbr\u003e12.10 Embeddability of Hadamard Matrices 259\u003cbr\u003e12.11 Embeddability of Hadamard Matrices of Order n − 8 260\u003cbr\u003e12.12 Embeddability of Hadamard Matrices of Order n − k 261\u003cbr\u003e12.13 Growth Problem for Hadamard Matrices 265\u003c\/p\u003e \u003cp\u003eA Hadamard Matrices 271\u003cbr\u003eB List of sds from Cyclotomy 295\u003cbr\u003eC Further Research Questions 301\u003c\/p\u003e \u003cp\u003eReferences 303\u003cbr\u003eIndex 313\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley","offers":[{"title":"Brand New","offer_id":52428613189912,"sku":"9781119520245","price":82.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781119520245.jpg?v=1784681535","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/hadamard-matrices-constructions-using-number-theory-and-linear-algebra-hardback-9781119520245","provider":"Freshly Printed Books","version":"1.0","type":"link"}