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Codes over rings [[electronic resource] ] : proceedings of the CIMPA Summer School : Ankara, Turkey, 18-29 August, 2008 / / editor, Patrick Solé
| Codes over rings [[electronic resource] ] : proceedings of the CIMPA Summer School : Ankara, Turkey, 18-29 August, 2008 / / editor, Patrick Solé |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, c2009 |
| Descrizione fisica | 1 online resource (201 p.) |
| Disciplina | 003/.54 |
| Altri autori (Persone) | SoléPatrick |
| Collana | Series on coding theory and cryptology |
| Soggetto topico |
Coding theory
Rings (Algebra) Quasi-Frobenius rings Number theory |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-282-75750-4
9786612757501 981-283-769-8 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; References; Partial Correlations of Sequences and Their Applications S. Bozta and P. Udaya; 1. Introduction and Background; 1.1. Outline of Paper; 2. Sequences and Correlations; 3. Rings, Trace Functions and Sequences; 3.1. Galois Ring Preliminaries; 3.2. Sequence Families- A, Band C; 4. The Partial Correlation and Its First Moment; 5. The Second Moment of the Partial Correlation Function; 6. Conclusions and Discussion; Acknowledgements; References; On the Structure of Cyclic and Negacyclic Codes over Finite Chain Rings H. Q. Dinh, S. R. Lopez-Per-mouth and S. Szabo
1. Introduction2. Chain Rings and Galois Rings; 3. Alternative Metrics for Codes over Finite Rings; 4. Constacyclic Codes over Arbitrary Commutative Finite Rings; 5. Simple-Root Cyclic and Negacyclic Codes over Finite Chain Rings; 6. Repeated-Root Cyclic and Negacyclic Codes over Finite Chain Rings; 7. Closing Remarks and A Few Generalizations; References; Linear Codes over Finite Chain Rings and Projective Hjelmslev Geometries T. Honold and 1. Landjev; 1. Introduction; 2. Modules over Finite Chain Rings; 2.1. Finite Chain Rings; 2.2. Structure of Finite Modules; 2.3. Free Modules 2.4. Counting Formulas3. Linear Codes over Finite Chain Rings; 3.1. Basic properties; 3.2. Code Spectra and Isomorphisms; 3.3. Mac Williams Identities; 4. Projective and Affine Hjelmslev Spaces; 4.1. Axiomatic Definition; 4.2. Coordinate Hjelmslev Geometries; 4.3. Multisets of Points in PHG(R~); 5. Linear Codes and Geometry; 5.1. Equivalence of Multisets of Points and Linear Codes; 5.2. Some Classes of Codes Defined Geometrically; 5.3. Generalized Gray Maps; 5.4. Linearly Representable Codes; 5.5. Homogeneous Weights and Strongly Regular Graphs; 6. Arcs in Projective Hjelmslev Planes 6.1. A General Upper Bound for the Size of an Arc6.2. Constructions for Arcs; 6.3. (k,2)-Arcs; 6.4. Dual Constructions; 6.5. Constructions Using Automorphisms; 6.6. Tables for Arcs in Geometries over Small Chain Rings; 7. Blocking Sets in Projective Hjelmslev Planes; 7.1. General Results; 7.2. Redei Type Blocking Sets; Acknowledgements; Bibliography; Foundations of Linear Codes Defined over Finite Modules: The Extension Theorem and the MacWilliams Identities 1. A. Wood; 1. Introduction; 2. Characters; 2.1. Basic results; 2.2. Additive form of characters; 2.3. Character modules 3. Finite rings3.1. Basic definitions; 3.2. Structure of finite rings; 3.3. Duality; 4. Mobius functions of posets; 4.1. Basic definitions; 4.2. Examples; 5. Linear codes over modules; sufficient conditions for the extension theorem; 5.1. Basic definitions; 5.2. The character module as alphabet: the case of Hamming weight; 5.3. Sufficient conditions: the case of Hamming weight; 5.4. Sufficient conditions: the case of rings; 5.5. Semi-linear transformations; 6. Necessary conditions for the extension theorem; 6.1. Statement of results; 6.2. Proof of Theorem 6.3 6.3. The strategy of Dinh and Lopez-Permouth and proofs of necessary conditions |
| Record Nr. | UNINA-9910456143303321 |
| Singapore ; ; Hackensack, NJ, : World Scientific, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Codes over rings [[electronic resource] ] : proceedings of the CIMPA Summer School : Ankara, Turkey, 18-29 August, 2008 / / editor, Patrick Solé
| Codes over rings [[electronic resource] ] : proceedings of the CIMPA Summer School : Ankara, Turkey, 18-29 August, 2008 / / editor, Patrick Solé |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, c2009 |
| Descrizione fisica | 1 online resource (201 p.) |
| Disciplina | 003/.54 |
| Altri autori (Persone) | SoléPatrick |
| Collana | Series on coding theory and cryptology |
| Soggetto topico |
Coding theory
Rings (Algebra) Quasi-Frobenius rings Number theory |
| ISBN |
1-282-75750-4
9786612757501 981-283-769-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; References; Partial Correlations of Sequences and Their Applications S. Bozta and P. Udaya; 1. Introduction and Background; 1.1. Outline of Paper; 2. Sequences and Correlations; 3. Rings, Trace Functions and Sequences; 3.1. Galois Ring Preliminaries; 3.2. Sequence Families- A, Band C; 4. The Partial Correlation and Its First Moment; 5. The Second Moment of the Partial Correlation Function; 6. Conclusions and Discussion; Acknowledgements; References; On the Structure of Cyclic and Negacyclic Codes over Finite Chain Rings H. Q. Dinh, S. R. Lopez-Per-mouth and S. Szabo
1. Introduction2. Chain Rings and Galois Rings; 3. Alternative Metrics for Codes over Finite Rings; 4. Constacyclic Codes over Arbitrary Commutative Finite Rings; 5. Simple-Root Cyclic and Negacyclic Codes over Finite Chain Rings; 6. Repeated-Root Cyclic and Negacyclic Codes over Finite Chain Rings; 7. Closing Remarks and A Few Generalizations; References; Linear Codes over Finite Chain Rings and Projective Hjelmslev Geometries T. Honold and 1. Landjev; 1. Introduction; 2. Modules over Finite Chain Rings; 2.1. Finite Chain Rings; 2.2. Structure of Finite Modules; 2.3. Free Modules 2.4. Counting Formulas3. Linear Codes over Finite Chain Rings; 3.1. Basic properties; 3.2. Code Spectra and Isomorphisms; 3.3. Mac Williams Identities; 4. Projective and Affine Hjelmslev Spaces; 4.1. Axiomatic Definition; 4.2. Coordinate Hjelmslev Geometries; 4.3. Multisets of Points in PHG(R~); 5. Linear Codes and Geometry; 5.1. Equivalence of Multisets of Points and Linear Codes; 5.2. Some Classes of Codes Defined Geometrically; 5.3. Generalized Gray Maps; 5.4. Linearly Representable Codes; 5.5. Homogeneous Weights and Strongly Regular Graphs; 6. Arcs in Projective Hjelmslev Planes 6.1. A General Upper Bound for the Size of an Arc6.2. Constructions for Arcs; 6.3. (k,2)-Arcs; 6.4. Dual Constructions; 6.5. Constructions Using Automorphisms; 6.6. Tables for Arcs in Geometries over Small Chain Rings; 7. Blocking Sets in Projective Hjelmslev Planes; 7.1. General Results; 7.2. Redei Type Blocking Sets; Acknowledgements; Bibliography; Foundations of Linear Codes Defined over Finite Modules: The Extension Theorem and the MacWilliams Identities 1. A. Wood; 1. Introduction; 2. Characters; 2.1. Basic results; 2.2. Additive form of characters; 2.3. Character modules 3. Finite rings3.1. Basic definitions; 3.2. Structure of finite rings; 3.3. Duality; 4. Mobius functions of posets; 4.1. Basic definitions; 4.2. Examples; 5. Linear codes over modules; sufficient conditions for the extension theorem; 5.1. Basic definitions; 5.2. The character module as alphabet: the case of Hamming weight; 5.3. Sufficient conditions: the case of Hamming weight; 5.4. Sufficient conditions: the case of rings; 5.5. Semi-linear transformations; 6. Necessary conditions for the extension theorem; 6.1. Statement of results; 6.2. Proof of Theorem 6.3 6.3. The strategy of Dinh and Lopez-Permouth and proofs of necessary conditions |
| Record Nr. | UNINA-9910780728903321 |
| Singapore ; ; Hackensack, NJ, : World Scientific, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Codes over rings : proceedings of the CIMPA Summer School : Ankara, Turkey, 18-29 August, 2008 / / editor, Patrick Sole
| Codes over rings : proceedings of the CIMPA Summer School : Ankara, Turkey, 18-29 August, 2008 / / editor, Patrick Sole |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, c2009 |
| Descrizione fisica | 1 online resource (201 p.) |
| Disciplina | 003/.54 |
| Altri autori (Persone) | SolePatrick |
| Collana | Series on coding theory and cryptology |
| Soggetto topico |
Coding theory
Rings (Algebra) Quasi-Frobenius rings Number theory |
| ISBN |
1-282-75750-4
9786612757501 981-283-769-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; References; Partial Correlations of Sequences and Their Applications S. Bozta and P. Udaya; 1. Introduction and Background; 1.1. Outline of Paper; 2. Sequences and Correlations; 3. Rings, Trace Functions and Sequences; 3.1. Galois Ring Preliminaries; 3.2. Sequence Families- A, Band C; 4. The Partial Correlation and Its First Moment; 5. The Second Moment of the Partial Correlation Function; 6. Conclusions and Discussion; Acknowledgements; References; On the Structure of Cyclic and Negacyclic Codes over Finite Chain Rings H. Q. Dinh, S. R. Lopez-Per-mouth and S. Szabo
1. Introduction2. Chain Rings and Galois Rings; 3. Alternative Metrics for Codes over Finite Rings; 4. Constacyclic Codes over Arbitrary Commutative Finite Rings; 5. Simple-Root Cyclic and Negacyclic Codes over Finite Chain Rings; 6. Repeated-Root Cyclic and Negacyclic Codes over Finite Chain Rings; 7. Closing Remarks and A Few Generalizations; References; Linear Codes over Finite Chain Rings and Projective Hjelmslev Geometries T. Honold and 1. Landjev; 1. Introduction; 2. Modules over Finite Chain Rings; 2.1. Finite Chain Rings; 2.2. Structure of Finite Modules; 2.3. Free Modules 2.4. Counting Formulas3. Linear Codes over Finite Chain Rings; 3.1. Basic properties; 3.2. Code Spectra and Isomorphisms; 3.3. Mac Williams Identities; 4. Projective and Affine Hjelmslev Spaces; 4.1. Axiomatic Definition; 4.2. Coordinate Hjelmslev Geometries; 4.3. Multisets of Points in PHG(R~); 5. Linear Codes and Geometry; 5.1. Equivalence of Multisets of Points and Linear Codes; 5.2. Some Classes of Codes Defined Geometrically; 5.3. Generalized Gray Maps; 5.4. Linearly Representable Codes; 5.5. Homogeneous Weights and Strongly Regular Graphs; 6. Arcs in Projective Hjelmslev Planes 6.1. A General Upper Bound for the Size of an Arc6.2. Constructions for Arcs; 6.3. (k,2)-Arcs; 6.4. Dual Constructions; 6.5. Constructions Using Automorphisms; 6.6. Tables for Arcs in Geometries over Small Chain Rings; 7. Blocking Sets in Projective Hjelmslev Planes; 7.1. General Results; 7.2. Redei Type Blocking Sets; Acknowledgements; Bibliography; Foundations of Linear Codes Defined over Finite Modules: The Extension Theorem and the MacWilliams Identities 1. A. Wood; 1. Introduction; 2. Characters; 2.1. Basic results; 2.2. Additive form of characters; 2.3. Character modules 3. Finite rings3.1. Basic definitions; 3.2. Structure of finite rings; 3.3. Duality; 4. Mobius functions of posets; 4.1. Basic definitions; 4.2. Examples; 5. Linear codes over modules; sufficient conditions for the extension theorem; 5.1. Basic definitions; 5.2. The character module as alphabet: the case of Hamming weight; 5.3. Sufficient conditions: the case of Hamming weight; 5.4. Sufficient conditions: the case of rings; 5.5. Semi-linear transformations; 6. Necessary conditions for the extension theorem; 6.1. Statement of results; 6.2. Proof of Theorem 6.3 6.3. The strategy of Dinh and Lopez-Permouth and proofs of necessary conditions |
| Record Nr. | UNINA-9910810533203321 |
| Singapore ; ; Hackensack, NJ, : World Scientific, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Quasi-Frobenius rings / W. K. Nicholson, M. F. Yousif
| Quasi-Frobenius rings / W. K. Nicholson, M. F. Yousif |
| Autore | Nicholson, W. Keith |
| Pubbl/distr/stampa | Cambridge : Cambridge University Press, 2003 |
| Descrizione fisica | xvii, 307 p. ; 24 cm |
| Disciplina | 512.4 |
| Altri autori (Persone) | Yousif, Mohamed F.author |
| Collana | Cambridge tracts in mathematics ; 158 |
| Soggetto topico | Quasi-Frobenius rings |
| ISBN | 0521815932 |
| Classificazione |
AMS 16-XX
AMS 16-02 AMS 16L99 LC QA251.5.N53 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991000497799707536 |
Nicholson, W. Keith
|
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| Cambridge : Cambridge University Press, 2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Quasi-Frobenius rings and generalizations : QF-3 and QF-1 rings / / Claus M. Ringel, H. Tachikawa
| Quasi-Frobenius rings and generalizations : QF-3 and QF-1 rings / / Claus M. Ringel, H. Tachikawa |
| Autore | Ringel Claus Michael |
| Edizione | [1st ed. 1973.] |
| Pubbl/distr/stampa | Berlin ; ; Heidelberg : , : Springer-Verlag, , [1973] |
| Descrizione fisica | 1 online resource (XII, 172 p.) |
| Disciplina | 512.4 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico | Quasi-Frobenius rings |
| ISBN | 3-540-37812-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preliminaries -- Semi-perfect rings -- Morita duality -- Left QF-3 rings -- The structure of QF-3 rings -- Are noetherian, left QF-3 rings artinian, so QF-3? -- Dominant dimension -- Conjectures arising from Nakayama's conjecture -- QF-3 rings and rings of finite representation type -- The double centralizer condition -- QF-13 rings -- QF-3 rings and categories of projective modules. |
| Record Nr. | UNISA-996466380203316 |
|
Ringel Claus Michael
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| Berlin ; ; Heidelberg : , : Springer-Verlag, , [1973] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Quasi-Frobenius rings and generalizations : QF-3 and QF-1 rings / Notes by Claus Michael Ringel
| Quasi-Frobenius rings and generalizations : QF-3 and QF-1 rings / Notes by Claus Michael Ringel |
| Autore | Tachikawa, Hiroyuki |
| Pubbl/distr/stampa | Berlin : Springer-Verlag, 1973 |
| Descrizione fisica | x, 172 p. ; 25 cm |
| Disciplina | 512.4 |
| Collana | Lecture notes in mathematics, 0075-8434 ; 351 |
| Soggetto topico |
Associative algebras
Associative rings Quasi-Frobenius rings |
| ISBN | 3540065016 |
| Classificazione |
AMS 16-02
AMS 16-XX AMS 16L99 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991001278179707536 |
|
Tachikawa, Hiroyuki
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| Berlin : Springer-Verlag, 1973 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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