Algebraic coding theory

Mathematics BSc
Course description
2013.

Eötvös Loránd University
Faculty of Science
Institute of Mathematics

Borromean Rings

All courses
Core courses
- Algebra, number theory
- Analysis
- Geometry
  - Geometry 1
- Discrete mathematics
  - Discrete mathematics 1
  - Discrete mathematics 2
- Elementary mathematics
  - Elementary mathematics 1
- Informatics
  - Prog. fundamentals
Pure mathematics
- Algebra, number theory
- Analysis
  - Analysis 3
  - Analysis 4
  - Applied analysis
    - Numerical analysis
    - Appl. anal. comp.
  - Differential equations
    - Differential equations
    - Partial diff. equations
  - Topology
    - Introduction
    - Algebraic topology
  - Complex analysis
  - Functional analysis
  - Function series
- Geometry
- Operations research
  - Operations research 1
  - Operations research 2
- Probability theory
- Informatics
- Computer science
- Foundations of math.
  - Set theory
  - Mathematical logic
Applied mathematics
- Analysis
  - Analysis 3
  - Analysis 4
  - Analysis 5
  - Applied analysis
  - Differential equations
    - Differential equations
    - Partial diff. equations
  - Complex analysis
  - Functional analysis
- Geometry
- Operations research
  - Operations research 1
  - Operations research 2
- Probability theory
- Applied modules
- Informatics
- Algorithms
- Algebra
- Elementary mathematics
  - Elementary mathematics 2
  - Elementary mathematics 3
- Foundations of math.
BSc: general information
Studies

Algebraic coding theory

Hours lect+pc	Credits lect+pc	Assessment	Specialization	Course code lect/pc	Semester	Status
2 + 0	2 + 0	exam	applied math.	mm1c1ak6e	6	recommended

Course coordinator

Péter Pál Pálfy
Department of Algebra and Number Theory
Institute of Mathematics

Strong	Weak	Prerequisites
Lecture
Lecture		Strong: Algebra3P-p (mm1c2al3m) or Algebra3P-a (mm1c2al3a)

Remarks

Syllabus designed by:

Péter Pál Pálfy, Department of Algebra and Number Theory, Institute of Mathematics.

Prerequisites

Classical and linear algebra, finite fields.

Course objectives

Introduction to the basic methods of error-correcting codes, an important application of abstract algebra.

Literature

E. R. Berlekamp: Algebraic Coding Theory. Aegean Park Pr; 1984.

Syllabus

Basic notions: Noisy channels, binary symmetric channel, error detection and error correction.
Block codes. Hamming distance, minimal distance.
Algebraic tools: finite fields (basic properties, existence and uniqueness, constructions, polynomials over finite fields).
Linear codes, generator and parity check matrices, Hamming codes.
Cyclic codes, described by means of ideals.
Codes and polynomials: generating and parity check polynomials, BCH codes, Reed-Solomon codes, quadratic residue codes, Reed-Muller codes, Golay codes, perfect codes.
Bounds on linear codes: Singleton, Hamming, Gilbert-Varshamov, Plotkin.
Decoding methods: syndromes, decoding BCH codes.
Error correction in digital media processing (compact disc).