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. Introduction -- 2. 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 Formulas -- 3. 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 Arc -- 6.2. 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 rings -- 3.1. 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 -- 7. Parameterized codes -- 7.1. Parameterized codes -- 7.2. Multiplicity functions -- 7.3. The weight mapping -- 7.4. Completion over IQ: virtual codes -- 7.5. Matrix representation for W -- 7.6. Field case -- 7.7. Matrix module case -- 8. Symmetrized weight compositions -- 8.1. Definitions -- 8.2. Averaged characters -- 8.3. Extension property for Frobenius bimodules -- 9. General weight functions -- 9.1. Homogeneous weight -- 9.2. A sufficient condition -- 9.3. Chain rings -- 9.4. Matrix rings -- 10. The MacWilliams identities: A model theorem.

10.1. Classical case of finite fields -- 10.2. Plan of attack -- 11. Mac Williams identities for additive codes -- 11.1. Fourier transform and Poisson summation formula -- 11.2. Additive codes -- 11.3. Biadditive forms -- 12. Duality for modules -- 12.1. Linear codes -- 12.2. Bilinear forms -- 12.3. The double annihilator property -- 12.4. The size condition -- 12.5. Generating characters -- 12.6. A degenerate case -- 13. Other weight enumerators -- 13.1. Full weight enumerators -- 13.2. Complete weight enumemtors -- 13.3. A degenerate case -- Acknowledgments -- References.