05636nam 2200733 a 450 991045614330332120200520144314.01-282-75750-49786612757501981-283-769-8(CKB)2490000000001587(EBL)1679527(OCoLC)613386705(SSID)ssj0000434601(PQKBManifestationID)11925652(PQKBTitleCode)TC0000434601(PQKBWorkID)10415462(PQKB)11515510(MiAaPQ)EBC1679527(WSP)00000527 (Au-PeEL)EBL1679527(CaPaEBR)ebr10422168(CaONFJC)MIL275750(EXLCZ)99249000000000158720090601d2009 uy 0engur|n|---|||||txtccrCodes over rings[electronic resource] proceedings of the CIMPA Summer School : Ankara, Turkey, 18-29 August, 2008 /editor, Patrick SoléSingapore ;Hackensack, NJ World Scientificc20091 online resource (201 p.)Series on coding theory and cryptology ;v. 6"This is the proceedings volume of the International Centre for Pure and Applied Mathematics Summer School course held in Ankara, Turkey, in August 2008"--Pref.981-283-768-X Includes bibliographical references.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. Szabo1. 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 Modules2.4. 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 Planes6.1. 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 modules3. 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 6.36.3. The strategy of Dinh and Lopez-Permouth and proofs of necessary conditionsThis is the proceedings volume of the International Centre for Pure and Applied Mathematics Summer School course held in Ankara, Turkey, in August 2008. Contributors include Bozta?, Udaya, Dinh, Ling, L�opez-Permouth, Szabo, Honold, Landjev and Wood. The aim is to present a survey in fundamental areas and highlight some recent results.Series on coding theory and cryptology ;6.Coding theoryCongressesRings (Algebra)CongressesQuasi-Frobenius ringsCongressesNumber theoryCongressesElectronic books.Coding theoryRings (Algebra)Quasi-Frobenius ringsNumber theory003/.54Solé Patrick862849International Centre for Pure and Applied Mathematics Summer SchoolMiAaPQMiAaPQMiAaPQBOOK9910456143303321Codes over rings1926215UNINA02285nam2 22004453i 450 UFI001706720231121125903.08843526251IT94-10182 19991201d1988 ||||0itac50 baitaitz01i xxxe z01n˜Il œCinquecento[a cura di Giuliano Brigantisaggi di Jaynie Anderson ... et al.]Riedizione accresciuta e aggiornataMilanoElecta19882 volumi (913 p. complessive)30 cmIn cofanetto.001RAV00111172001 ˜La œpittura in Italia\comitato scientifico: Carlo Bertelli et al.!001RAV02465872000 11001RAV02465892000 22001UFI00170752000 1[a cura di Giuliano Brigantisaggi di Jaynie Anderson ... et al.!1001UFI00170762000 2[a cura di Giuliano Brigantisaggi di Jaynie Anderson ... et al.!2PitturaItaliaStoriaSec. 16.FIRRMLC403327I759.509031Pittura italiana. 1500-159920759.509031Pittura italiana. 1500-159921Briganti, GiulianoCFIV017610Anderson, JaynieRAVV066870ITIT-0119991201IT-RM0289 IT-RM0211 IT-FR0084 IT-FR0017 Biblioteca Statale A. BaldiniRM0289 Fondazione Marco BessoRM0211 Biblioteca Del Monumento Nazionale Di MontecassinoFR0084 Biblioteca umanistica Giorgio ApreaFR0017 UFI0017067Biblioteca umanistica Giorgio Aprea 52PFR 759 Ita.3.1 52PFR 759 Ita.3.2 52S.L. 759.5 Pit.Ita.Ele.4.1 52S.L. 759.5 Pit.Ita.Ele.4.2 52CIS S.L.759.5 Pit.Ita.Cin.1 52VM 0000190355 VM barcode:00061163. - Inventario:20077 FLSVMB 2003011720121204 52CIS S.L.759.5 Pit.Ita.Cin.2 52VM 0000190345 VM barcode:00055859. - Inventario:20077 FLSVMB 2005070620121204 04 14 25 52Cinquecento74775UNICAS