LEADER 05596nam 2200733 a 450 001 9910810533203321 005 20200520144314.0 010 $a1-282-75750-4 010 $a9786612757501 010 $a981-283-769-8 035 $a(CKB)2490000000001587 035 $a(EBL)1679527 035 $a(OCoLC)613386705 035 $a(SSID)ssj0000434601 035 $a(PQKBManifestationID)11925652 035 $a(PQKBTitleCode)TC0000434601 035 $a(PQKBWorkID)10415462 035 $a(PQKB)11515510 035 $a(MiAaPQ)EBC1679527 035 $a(WSP)00000527 035 $a(Au-PeEL)EBL1679527 035 $a(CaPaEBR)ebr10422168 035 $a(CaONFJC)MIL275750 035 $a(EXLCZ)992490000000001587 100 $a20090601d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aCodes over rings $eproceedings of the CIMPA Summer School : Ankara, Turkey, 18-29 August, 2008 /$feditor, Patrick Sole 205 $a1st ed. 210 $aSingapore ;$aHackensack, NJ $cWorld Scientific$dc2009 215 $a1 online resource (201 p.) 225 1 $aSeries on coding theory and cryptology ;$vv. 6 300 $a"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. 311 $a981-283-768-X 320 $aIncludes bibliographical references. 327 $aContents; 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 327 $a1. 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 327 $a2.4. 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 327 $a6.1. 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 327 $a3. 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 6.3 327 $a6.3. The strategy of Dinh and Lopez-Permouth and proofs of necessary conditions 330 $aThis is the proceedings volume of the International Centre for Pure and Applied Mathematics Summer School course held in Ankara, Turkey, in August 2008. Contributors include Bozta?, Udaya, Dinh, Ling, L?opez-Permouth, Szabo, Honold, Landjev and Wood. The aim is to present a survey in fundamental areas and highlight some recent results. 410 0$aSeries on coding theory and cryptology ;$v6. 606 $aCoding theory$vCongresses 606 $aRings (Algebra)$vCongresses 606 $aQuasi-Frobenius rings$vCongresses 606 $aNumber theory$vCongresses 615 0$aCoding theory 615 0$aRings (Algebra) 615 0$aQuasi-Frobenius rings 615 0$aNumber theory 676 $a003/.54 701 $aSole$b Patrick$01661226 712 12$aInternational Centre for Pure and Applied Mathematics Summer School 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910810533203321 996 $aCodes over rings$94017026 997 $aUNINA