Coding

Fall Semester 2002-2004

Instructor: J.A. Antoniadis

Class Time: Wednesday 9-11, Friday 11-1 Room: Α105

Grading

The scores will be weighted as follows:
Homework: 20%, Lecture: 20%, Final exam: 60%

Notes

Chapter 1

1. Prelimaries [doc] [ps]
2. Linear codes [doc] [ps]
3. Hamming codes [doc] [ps]
4. Cyclic codes [doc] [ps]
5. More οn cyclic codes [doc] [ps]
6. BCH codes [doc] [ps]
7. Reed-Muller codes [doc] [ps]
8. Quadratic Residue (QR) codes [doc] [ps]
9. MDS codes [doc] [ps]
10. Modifying codes [doc] [ps]

Chapter 2: Algebraic curves and coding

1. Algebraic curves [doc] [ps]
2. Functions over algebraic curves [doc] [ps]
3. Algebraic geometry codes [doc] [ps]
4. Asyptotically good sequences of codes and curves [doc] [ps]
5. Order functions [doc] [ps]

Lectures

During the course each graduate student will give a lecture on coding

Christos Zohios' lecture: Codes and Latin squares [dvi] [ps] [pdf]
Maria Christopoulou's lecture: Weight enumerators [dvi] [ps] [pdf]
Marios Magioladitis' lecture: The main linear coding theory problem [doc] [ps] [pdf]

Homework

Homework 1 (PDF) Homework 4 (PDF) Homework 7 (PDF)
Homework 2 (PDF) Homework 5 (PDF)
Homework 3 (PDF) Homework 6 (PDF)

Final exam

The final exam took place on February 7th 2003
The questions: [doc] [ps] (in Greek)

Textbook

Foto Afrati, Introduction to information theory Symmetria, Athens 1994

Bibliography

1. J.A. Antoniadis Algebraic Curves and Coding Lecture on Summer School of Mathematics 200 (in PDF format)
2. J.A. Antoniadis Applied Algebra Marios Magioladitis' notes, Heraklion 2000 (in Microsoft Word format)
3. Foto Afrati, Introduction to information theory Symmetria, Athens 1994
4. Marios Magioladitis Algebraic Curves, Riemann hypothesis and coding Diploma thesis, Heraklion 2002
5. Raymond Hill, A First Course in Coding Theory Clarendon Press, Oxford 2001
6. R. Lidl, G. Pilz, Applied Abstract Algebra Springer-Verlag, New York 1998
7. F. J. MacWilliams, N.J.A. Sloane, Introduction to Coding Theory Second Edition, Springer-Verlag, Berlin 1992
8. Carlos Moreno, Algebraic Curves over Finite Fields Cambridge Univ. Press, Cambridge 1993
9. H. Niederreiter, C. Xing, Rational Points on Curves over Finite Fields LMS 285, London 2001
10. Oliver Pretzel, Codes and Algebraic Curves Clarendon Press, Oxford 1998
11. Oliver Pretzel, The Theory of Error-Correcting North-Holland, Amsterdam 1988
12. Steven Roman, Coding and Information Theory Springer-Verlag, New York 1992
13. Henning Stichtenoth, Algebraic Function Fields and Codes Springer-Verlag, Berlin 1993

Maintenance at: Marios Magioladitis