[Ελληνικά / Greek]

# Coding

Fall semester 2003-2004

**Instructor**: J.A. Antoniadis

**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.

## Grading

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

Maintenance at: Marios
Magioladitis