[Ελληνικά / Greek]

# Coding

Fall semester 2003-2004

Class Time: Monday 9-11, Wednesday 9-11 Room: A103
Exersices: Friday 7-9 Room: B211

Here you can find the course's web page as taught in 2002.

The scores will be weighted as follows:

For students of the Mathematics Department
Homework: 20%, Lecture: 30%, Final exam: 50%
For students of the Computer Science Department
Homework: 20%, Project: 40%, Final exam: 40%

## Notes

Chapter 1 [doc] [ps] [pdf]

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 gave a lecture on coding

Marios Magioladitis' lecture: The main linear coding theory problem [doc] [ps] [pdf]
Andreas Tsilifonis' lecture: The binary Golay [23, 12, 7]-code
Katerina Kouta's lecture: Decoding BCH and Reed-Solomon codes
Christos Saroglou's lecture: Quadratic Residue (QR) codes [doc] [ps] [pdf]

## Projects

During the course each graduate student of the Computer Science Department made a project based on a paper. The program reports follow.

Anastasia - Vasiliki Euaggelatou and Euriklis Kounalakis: Soft Decision Majority Decoding of Reed-Muller Codes
Manos Moshos and Kyriaki Karadimou: A Class of Array Codes Correcting Multiple Column Erasures
Haridimos Kondilakis and Demetris Simos: Low-Density Parity-Check (Gallager) Codes
Alkiviadis Simeonidis and George Fotiadis: Sort and match Algorithm for soft-decision decoding

## Homework

• Homework 1 [pdf] [ps].
• Homework 2 [pdf] [ps].
• Homework 3 [pdf] [ps].
• Homework 4 [pdf] [ps].
• Homework 5 [pdf] [ps].
• Homework 8 [pdf] [ps].
• Homework 2 (HY438-2002) [pdf] [ps].
• Homework 5 (HY438-2001) [pdf] [ps].
• Homework 4 (HY438-2002, new version) [pdf] [ps].
• Homework 5 (HY438-2002, new version) [pdf] [ps].

### Solutions

• Homework 1 [pdf] [ps].
• Homework 2 [pdf] [ps].
• Homework 3 [pdf] [ps].
• Homework 4 [pdf] [ps].
• Homework 5 [pdf] [ps].
• Homework 2 (HY438-2002) [pdf] [ps].
• Homework 5 (HY438-2001) [pdf] [ps].
• Homework 4 (HY438-2002, new version) [pdf] [ps].
• Homework 5 (HY438-2002, new version) [pdf] [ps].

## Final exam

The final exam took place on February 3th 2004
The questions: [doc] [ps] [pdf] (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