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Umfang: 1 online resource (484 pages)

ISBN: 9780443135187

Anmerkung: Front Cover -- Sequences and the de Bruijn Graph -- Copyright -- Contents -- Preface -- 1 Introduction -- 1.1 Some concepts in finite fields and number theory -- 1.2 Codes, graphs, and sequences -- 1.3 The de Bruijn graph and feedback shift registers -- 1.4 Overview of the chapters -- 1.5 Notes -- References -- 2 LFSR sequences -- 2.1 Sequence length and polynomial representation -- 2.2 Maximum length linear shift-register sequences -- 2.3 Powers of irreducible polynomials -- 2.4 Patterns with distinct differences -- 2.5 Notes -- References -- 3 Cycles and the nonlinear theory -- 3.1 Cycles from feedback shift registers -- 3.2 Enumeration methods for polynomials and cycles -- 3.3 Maximum number of cycles in a state diagram -- 3.4 Notes -- References -- 4 Constructions of full cycles -- 4.1 Enumeration of all Eulerian cycles -- 4.2 The D-morphism and recursive constructions -- 4.3 Merging cycles of large factors -- 4.4 Notes -- References -- 5 Linear complexity of sequences -- 5.1 Binary sequences whose length is 2n -- 5.2 Complexity of binary de Bruijn sequences -- 5.3 Sequences over pm whose length is pn, p prime -- 5.4 Complexity of non-binary de Bruijn sequences -- 5.5 Notes -- References -- 6 Classification of sequences -- 6.1 Classification of sequences with length 2n−1 -- 6.2 Classification of de Bruijn sequences -- 6.3 Classification of balanced sequences -- 6.4 The depth of a word -- 6.5 Notes -- References -- 7 One-dimensional applications -- 7.1 Stream ciphers -- 7.2 VLSI testing -- 7.3 Single-track Gray codes -- 7.4 Rotating-table games -- 7.5 Notes -- References -- 8 DNA sequences and DNA codes -- 8.1 The genome assembly -- 8.2 DNA storage codes -- 8.3 Constant-weight de Bruijn sequences -- 8.4 Reconstruction of a sequence from subsequences -- 8.5 Synchronization codes -- 8.6 Notes -- References -- 9 Two-dimensional arrays. , 9.1 Graph representations of perfect maps -- 9.2 Constructions by merging cycles -- 9.3 Pseudo-random arrays -- 9.4 Recursive constructions for perfect maps -- 9.5 Two-dimensional arrays with distinct differences -- 9.6 Notes -- References -- 10 Two-dimensional applications -- 10.1 Robust self-location two-dimensional patterns -- 10.2 Key predistribution for sensor networks -- 10.3 Folding of one-dimensional sequences -- 10.4 Notes -- References -- 11 Unique path property graphs -- 11.1 Basic properties of UPP graphs -- 11.2 Constructions for UPP graphs -- 11.3 Cycles and factors in UPP graphs -- 11.4 Notes -- References -- 12 Interconnection networks -- 12.1 The shuffle-exchange network -- 12.2 Multistage interconnection networks -- 12.3 Multistage permutation networks -- 12.4 Layouts -- 12.5 Notes -- References -- Index -- Back Cover.

Weitere Ausg.: Print version: Etzion, Tuvi Sequences and the de Bruijn Graph San Diego : Elsevier Science & Technology,c2024 ISBN 9780443135170

Sprache: Englisch