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  • 1
    Online Resource
    Online Resource
    Codes and modular forms : a dictionary (2019)
    Singapore : World Scientific Publishing Co. Pte. Ltd
    Details
    UID:
    (DE-627)1737719908
    Format: 1 Online-Ressource (232 p) , ill
    ISBN: 9789811212925
    Content: "There are connections between invariant theory and modular forms since the times of Felix Klein, in the 19th century, connections between codes and lattices since the 1960's. The aim of the book is to explore the interplay between codes and modular forms. Here modular form is understood in a wide sense (Jacobi forms, Siegel forms, Hilbert forms). Codes comprises not only linear spaces over finite fields but modules over some commutative rings. The connection between codes over finite fields and lattices has been well documented since the 1970s. Due to an avalanche of results on codes over rings since the 1990's there is a need for an update at book level."--Publisher's website
    Content: Codes vs lattices: a dictionary -- Modular forms in one variable -- Siegel modular forms -- Jacobi forms -- Automorphic forms over number fields -- Construction of self-dual codes of higher lengths over ℤ2m and determination of Jacobi forms -- Byte weight enumerators of codes and modular forms of genus g -- Byte weight enumerators of codes over 𝔽p and modular forms over a totally real field.
    Note: "November 2019." , Includes bibliographical references , Mode of access: World Wide Web. , System requirements: Adobe Acrobat Reader.
    Additional Edition: 9811212910
    Additional Edition: 9789811212918
    Additional Edition: Erscheint auch als Druck-Ausgabe 9811212910
    Additional Edition: 9789811212918
    Language: English
    Keywords: Electronic books
    URL: Access to full text is restricted to subscribers
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  • 2
    Online Resource
    Online Resource
    Codes and modular forms : a dictionary (2019)
    Singapore : World Scientific Publishing Company Pte. Limited
    Details
    UID:
    (DE-604)BV046808161
    Format: 1 online resource (232 pages) , illustrations
    ISBN: 9789811212925
    Content: "There are connections between invariant theory and modular forms since the times of Felix Klein, in the 19th century, connections between codes and lattices since the 1960's. The aim of the book is to explore the interplay between codes and modular forms. Here modular form is understood in a wide sense (Jacobi forms, Siegel forms, Hilbert forms). Codes comprises not only linear spaces over finite fields but modules over some commutative rings. The connection between codes over finite fields and lattices has been well documented since the 1970s. Due to an avalanche of results on codes over rings since the 1990's there is a need for an update at book level."--Publisher's website
    Note: Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader. - "November 2019." , Codes vs lattices: a dictionary -- Modular forms in one variable -- Siegel modular forms -- Jacobi forms -- Automorphic forms over number fields -- Construction of self-dual codes of higher lengths over ́"Þ2m and determination of Jacobi forms -- Byte weight enumerators of codes and modular forms of genus g -- Byte weight enumerators of codes over ̧"ưp and modular forms over a totally real field , Includes bibliographical references
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 9789811212918
    Language: English
    DOI: 10.1142/11628
    URL: Volltext  (URL des Erstveröffentlichers)
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  • 3
    Online Resource
    Online Resource
    Codes and rings : theory and practice (2017)
    London : Academic Press, an imprint of Elsevier
    Details
    UID:
    (DE-604)BV044989500
    Format: 1 online resource (320 pages)
    ISBN: 9780128133910
    Note: Description based on publisher supplied metadata and other sources
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-0-12-813388-0
    Language: English
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  • 4
    Book
    Book
    Codes and rings : theory and practice (2017)
    London : Academic Press, an imprint of Elsevier
    Details
    UID:
    (DE-627)1627449272
    Format: xv, 301 Seiten , 23 cm
    ISBN: 9780128133880
    Series Statement: Pure and applied mathematics
    Additional Edition: Erscheint auch als Online-Ausgabe Codes and rings London$aSan Diego, CA$aCambridge, MA$aKidlington, Oxford : Academic Press, an imprint of Elsevier, 2017 9780128133910
    Additional Edition: 0128133910
    Language: English
    Keywords: Codierungstheorie ; Algebraischer Ring ; Ring ; Codierungstheorie
    URL: Inhaltsverzeichnis
    URL: Inhaltstext
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  • 5
    Online Resource
    Online Resource
    Codes and rings : theory and practice (2017)
    London$aSan Diego, CA$aCambridge, MA$aKidlington, Oxford : Academic Press, an imprint of Elsevier
    Details
    UID:
    (DE-627)1655314955
    Format: 1 Online-Ressource (xv, 301 Seiten)
    Edition: Online-Ausgabe
    ISBN: 9780128133910 , 0128133910
    Series Statement: Pure and applied mathematics
    Content: Codes and Rings: Theory and Practice is a systematic review of literature that focuses on codes over rings and rings acting on codes. Since the breakthrough works on quaternary codes in the 1990s, two decades of research have moved the field far beyond its original periphery. This book fills this gap by consolidating results scattered in the literature, addressing classical as well as applied aspects of rings and coding theory. New research covered by the book encompasses skew cyclic codes, decomposition theory of quasi-cyclic codes and related codes and duality over Frobenius rings. Primarily suitable for ring theorists at PhD level engaged in application research and coding theorists interested in algebraic foundations, the work is also valuable to computational scientists and working cryptologists in the area
    Note: Includes bibliographical references and index. - Online resource; title from PDF title page (EBSCO, viewed June 26, 2017. Vendor-supplied metadata
    Additional Edition: 9780128133880
    Additional Edition: 0128133880
    Additional Edition: Erscheint auch als Druck-Ausgabe Shi, Minjia Codes and rings London : Academic Press, an imprint of Elsevier, 2017 9780128133880
    Language: English
    Keywords: Codierungstheorie ; Algebraischer Ring ; Ring ; Codierungstheorie ; Ring ; Codierungstheorie ; Electronic book ; Electronic books ; Electronic books
    DOI: 10.1016/C2016-0-04429-7
    URL: Volltext
    URL: lizenzpflichtig
    URL: Volltext  (lizenzpflichtig)
    URL: Inhaltstext
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  • 6
    Online Resource
    Online Resource
    Codes and Rings : Theory and Practice (2017)
    San Diego : Elsevier Science
    Details
    UID:
    (DE-627)891130659
    Format: 1 Online-Ressource (320 pages)
    ISBN: 9780128133910
    Series Statement: Pure and Applied Mathematics v.Volume -
    Content: Front Cover -- Codes and Rings -- Copyright -- Contents -- Foreword -- Introduction -- 1 Motivation -- 1.1 The Geometry of Codes -- 1.2 Sequences -- 1.2.1 Periodic Correlation -- 1.3 Lattices -- 1.4 Maps -- 1.4.1 Prehistory -- 1.4.2 History -- 1.4.3 Present -- 1.5 Designs -- References -- 2 Rings -- 2.1 Basic Rings -- 2.2 Local Rings -- 2.3 Galois Rings -- 2.3.1 Hensel Lifting -- 2.3.2 Bottom-up -- 2.3.3 Top-down -- 2.3.4 Multiplicative Structure -- 2.4 Skew Polynomial Rings -- 2.5 Chain Rings -- 2.6 Frobenius Rings -- References -- 3 Distances -- 3.1 The Lee Metric -- 3.1.1 The Sphere-packing Bound -- 3.1.2 A Plotkin-like Bound -- 3.1.3 A Singleton-like Bound -- 3.1.4 Other Bounds -- 3.2 The Homogeneous Metric -- 3.2.1 Sphere-packing Bound -- 3.2.1.1 A Plotkin-like Bound -- 3.2.1.2 A Singleton-like Bound -- 3.2.1.3 Other Bounds -- 3.3 Hamming Metric -- 3.3.1 Codes over Frobenius Rings -- 3.3.2 A Griesmer-like Bound -- 3.3.3 A Singleton-like Bound -- References -- 4 Few Weight Codes -- 4.1 One-weight Codes -- 4.1.1 Preliminaries -- 4.1.2 One-homogeneous Weight Codes over Finite Chain Rings -- 4.2 Two-weight Codes -- 4.2.1 Linear Codes and Geometries over Finite Frobenius Rings -- 4.2.2 Two-weight Codes over a Finite Frobenius Ring -- 4.2.3 Two-weight Codes and Strongly Regular Graphs -- 4.2.4 Constructions -- 4.2.5 Properties of Codes with Two Homogeneous Weights -- 4.2.6 Gray Isometries -- 4.3 On Two-weight Z2k-codes -- 4.3.1 Background -- 4.3.1.1 Graph Theory -- 4.3.2 Coding Theory -- 4.3.3 Z2k-codes and Syndrome Graphs -- 4.3.4 Two-weight Z4-codes -- References -- 5 Linear Codes -- 5.1 Chain Rings -- 5.1.1 Generator Matrix -- 5.1.2 Dual Code -- 5.1.3 Free Codes -- 5.2 Modular Independence -- References -- 6 Self-dual Codes -- 6.1 Chain Rings -- 6.1.1 Existence Conditions -- 6.1.2 Type II Codes -- 6.2 Commutative Frobenius Rings
    Content: 6.2.1 CRT Theory -- 6.2.2 Existence Results -- 6.3 Noncommutative Frobenius Rings -- References -- 7 Cyclic Codes -- 7.1 Splitting Codes -- 7.1.1 Divisors of xn-1 -- 7.1.2 A Characterization of Splitting Cyclic Codes -- 7.2 Polycyclic Codes -- 7.2.1 Sequential Codes -- 7.3 Multivariable Codes -- 7.3.1 Multivariable Semisimple Codes -- 7.3.1.1 Decomposition of R[X1,…,Xr]/ -- 7.3.1.2 Description of the Codes -- 7.3.1.3 Hamming Distance of the Codes -- 7.3.2 Dual Codes of Abelian Semisimple Codes -- 7.3.3 Self-dual Abelian Semisimple Codes -- References -- 8 Quasicyclic Codes -- 8.1 Quasicyclic Codes over Finite Fields -- 8.1.1 Facts and Notation -- 8.1.2 Quasicyclic Codes -- 8.1.3 The Ring R(F,m) -- 8.1.4 Trace Formula -- 8.1.5 Applications -- 8.1.5.1 Quasicyclic Codes of Index 2 -- 8.1.5.2 Case m=2 and the (u+v|u-v) Construction -- 8.1.5.3 Case m=3 and Turyn's Construction -- 8.1.5.4 Case m=4 -- 8.1.5.5 Case m=5 -- 8.1.5.6 Case m=7 -- 8.1.5.7 The Vandermonde Construction -- 8.1.6 Self-dual Binary Codes -- Appendix: Algebraic Characterization -- 8.2 Quasicyclic Codes and Chain Rings -- 8.2.1 Notation and De nitions -- 8.2.1.1 Rings -- 8.2.1.2 Codes -- 8.2.2 Quasicyclic Codes -- 8.2.3 The Ring R(A,m) -- 8.2.4 Fourier Transform -- 8.2.5 Applications -- 8.2.5.1 Quasicyclic Codes of Index 2 -- 8.2.5.2 Case m=3 and the Leech Lattice -- 8.2.5.3 Case m=6 and the Golay Code -- 8.2.5.4 The Vandermonde Construction -- 8.2.6 Codes over Z2k -- Appendix: Algebraic Characterization -- 8.2.7 Case q=m=2 and the Squaring Construction -- 8.2.8 Case q=m=3 and the (u+v+w| 2u+v| u) Construction -- 8.3 Asymptotic Bounds -- 8.3.1 Known Facts and Notation -- 8.3.2 Good Self-dual Quasicyclic Codes Exist -- 8.3.3 Asymptotic Analysis -- References -- 9 Quasitwisted Codes -- 9.1 On Quasitwisted Codes over Finite Fields -- 9.1.1 Basic Theory
    Content: 9.1.2 Decomposition of QT Codes -- 9.1.3 Dual Codes of QT Codes -- 9.1.3.1 Case when λ=±1 -- 9.1.3.2 Case when λ±1 -- 9.1.4 Discrete Fourier Transform -- 9.1.5 Construction Formula -- 9.1.6 Examples -- 9.2 Quasitwisted Codes with Constacyclic Constituent Codes -- 9.2.1 The λ-Circulant Set Decomposition of a λ-Constacyclic Code -- 9.2.2 Quasitwisted Codes with Constacyclic Constituent Codes -- 9.2.3 The Generator Polynomial of θ(ψ(C)) -- 9.2.4 Examples -- References -- 10 Generalized Quasicyclic Codes -- 10.1 Background on QC and GQC Codes -- 10.2 Concatenated Structure and Trace Representation -- 10.3 Self-dual and LCD Cases -- 10.4 Asymptotics for LCD codes -- 10.5 Asymptotics for Self-dual Codes -- 10.5.1 Combinatorial Bounds -- 10.5.1.1 Cubic Construction -- 10.5.1.2 Quintic Construction -- 10.5.1.3 Asymptotic Bounds -- 10.5.1.4 Cubic Codes -- 10.5.1.5 Quintic Codes -- 10.5.1.6 GQC Codes -- References -- 11 Skew Cyclic Codes -- 11.1 Ideal Codes -- 11.1.1 Duals of θ-Cyclic Codes -- 11.1.2 The Bound of a Skew Polynomial -- 11.2 Derivations -- 11.3 Skew (Consta)cyclic Codes over Chain Rings -- 11.3.1 De nitions and Basic Properties -- 11.3.2 Skew Constacyclic Codes Generated by Monic Right Divisors of xn-λ -- 11.3.2.1 Properties of Skew Constacyclic Codes Generated by Monic Right Divisors of xn-λ -- 11.4 Module Codes -- 11.4.1 Skew Cyclic Codes -- 11.4.2 Asymptotic Bounds -- 11.4.3 Counting Codes -- 11.5 Application to Lattices -- 11.5.1 Quotients of Cyclic Division Algebras -- 11.5.2 Construction A -- 11.5.3 Examples -- References -- 12 MDR Codes -- 12.1 Introduction -- 12.2 Decomposition of a Code -- 12.3 Characterization of MDR Codes -- 12.4 The Submodules Quotient -- 12.5 The Dual Code -- References -- 13 Convolutional Codes -- 13.1 Convolutional Codes -- 13.2 Semisimple Modules -- 13.3 p-Generator Sequence and p-Basis
    Content: 13.3.1 p-Generator Sequence in Zpr -- 13.3.2 Generalization to the Polynomial Ring -- 13.4 Convolutional Codes over Rings -- 13.4.1 Background -- 13.4.2 Representation by the Delay Operator -- 13.4.3 Properties of Generator Matrices -- 13.4.4 Minimal p-Encoder -- 13.5 MDS Convolutional Codes Over a Finite Ring -- 13.5.1 Introduction -- 13.5.2 The Generalized Singleton Bound for Codes over a Finite Ring -- 13.6 Construction of MDS Convolutional Codes over a Finite Ring -- 13.6.1 Characterization of Free MDS Codes -- 13.6.2 Construction of MDS Codes -- References -- 14 Character Sums -- 14.1 Gauss Sums over Quasi-Frobenius Rings -- 14.1.1 Gauss Sums over Local Rings -- 14.1.2 Quasi-Frobenius Rings -- 14.2 Weil Sums -- 14.2.1 Weil/Carlitz-Uchiyama Bound -- 14.2.2 Galois Ring Weil Sums -- 14.2.3 Low Correlation Sequences -- 14.3 Pseudo-random Sequences -- 14.3.1 Preliminaries -- 14.3.2 DFT and the Local Weil Bound -- 14.3.3 Polynomials over the Galois Ring GR(2l,m) -- 14.3.4 Binary Sequences over Z8 -- 14.3.5 Binary Sequences of Period 2m-1 -- 14.3.6 Binary Codes and Sequences of Maximal Length -- 14.3.7 Nonbinary Codes of Maximal Length -- 14.3.8 Biphase Sequences -- References -- Index -- Back Cover
    Additional Edition: 9780128133880
    Additional Edition: Erscheint auch als Druck-Ausgabe Shi, Minjia Codes and Rings : Theory and Practice San Diego : Elsevier Science,c2017 9780128133880
    Language: English
    URL: Volltext  (lizenzpflichtig)
    URL: Inhaltstext
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  • 7
    Online Resource
    Online Resource
    Cyclic codes over the ring $$ Z_P^2 } $$ of length p e (2008)
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    Details
    UID:
    (DE-101)110538151X
    Format: Online-Ressource , online resource.
    ISSN: 1993-0615 , 1993-0615
    In: volume:25
    In: number:5
    In: day:1
    In: month:9
    In: year:2008
    In: pages:636-640
    In: date:9.2008
    In: Journal of electronics (China), Beijing : Science Pr., 1984-, 25, Heft 5 (1.9.2008), 636-640, 9.2008, 1993-0615
    Language: English
    DOI: 10.1007/s11767-007-0071-7
    URN: urn:nbn:de:1111-2016070412459
    URL: https://doi.org/10.1007/s11767-007-0071-7
    URL: https://nbn-resolving.org/urn:nbn:de:1111-2016070412459
    URL: https://d-nb.info/110538151X/34
    URL: http://dx.doi.org/10.1007/s11767-007-0071-7
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  • 8
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    Online Resource
    Several classes of asymptotically good quasi-twisted codes with a low index (2021)
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    UID:
    (DE-101)1242087184
    Format: Online-Ressource , online resource.
    ISSN: 1865-2085 , 1865-2085
    In: day:4
    In: month:6
    In: year:2021
    In: pages:1-18
    In: Journal of applied mathematics and computing, Berlin ; Heidelberg : Springer, 2006-, (4.6.2021), 1-18, 1865-2085
    Language: English
    DOI: 10.1007/s12190-021-01564-3
    URN: urn:nbn:de:101:1-2021092820263630241843
    URL: https://doi.org/10.1007/s12190-021-01564-3
    URL: https://nbn-resolving.org/urn:nbn:de:101:1-2021092820263630241843
    URL: https://d-nb.info/1242087184/34
    URL: https://doi.org/10.1007/s12190-021-01564-3
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  • 9
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    Repeated-Root Constacyclic Codes of Length $$k\ell p^s$$ k ℓ p s (2019)
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    Details
    UID:
    (DE-101)1200013166
    Format: Online-Ressource , online resource.
    ISSN: 2180-4206 , 2180-4206
    In: day:14
    In: month:6
    In: year:2019
    In: pages:1-19
    In: Bulletin of the Malaysian Mathematical Sciences Society, [Singapore] : Springer Singapore, [2000]-, (14.6.2019), 1-19, 2180-4206
    Language: English
    DOI: 10.1007/s40840-019-00787-9
    URN: urn:nbn:de:101:1-2019111921523521313987
    URL: https://doi.org/10.1007/s40840-019-00787-9
    URL: https://nbn-resolving.org/urn:nbn:de:101:1-2019111921523521313987
    URL: https://d-nb.info/1200013166/34
    URL: https://doi.org/10.1007/s40840-019-00787-9
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  • 10
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    Online Resource
    Three-weight codes, triple sum sets, and strongly walk regular graphs (2019)
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    Details
    UID:
    (DE-101)1182963641
    Format: Online-Ressource , online resource.
    ISSN: 1573-7586 , 1573-7586
    In: day:16
    In: month:3
    In: year:2019
    In: pages:1-10
    In: Designs, codes and cryptography, Dordrecht [u.a.] : Springer Science + Business Media B.V, 1991-, (16.3.2019), 1-10, 1573-7586
    Language: English
    DOI: 10.1007/s10623-019-00628-7
    URN: urn:nbn:de:101:1-2019040820265838731030
    URL: https://doi.org/10.1007/s10623-019-00628-7
    URL: https://nbn-resolving.org/urn:nbn:de:101:1-2019040820265838731030
    URL: https://d-nb.info/1182963641/34
    URL: https://doi.org/10.1007/s10623-019-00628-7
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