MATH 460 Spring 2012
Syllabus

Course: MATH 460, Spring 2012, 3 credits.

Lecturer: Dr. Anton Betten, Weber 207, email betten at math dot colostate dot edu

MATH460 Web Site: http://www.math.colostate.edu/ ∼ betten/MATH460

Office Hours and location: Weber 17 Monday 11 am.

Prerequisite: MATH 360, MATH369, STAT321 (not enforced).

Textbook: None required. The section headings below refer to Steven Roman: Coding and Information Theory. Springer.

Lectures: MWF 9am in Engr E 206

Course Content: Coding Theory, Information Theory.

Grading: Based on two student presentations, in weeks 5 and 14. No final. Some homework. Student presentation could include programming topics.

Syllabus:

Week 1
Introduction: Check systems and orthomorphisms.

Klara Schuhmann and the Dihedral group.
Week 2
Hamming space, Finite Projective space
4.2 Minimum distance decoding, sphere packing bound, Hamming codes
Week 3
4.3 Equivalence of codes. Families of codes, new codes from old. The automorphism group of a code
Week 4
4.4 Codes and Designs
Week 5
Student Presentations
Week 6
4.5 The Main Coding Theory Problem, lower and upper bounds. Gilbert-Varshamov, Singleton, Sphere-packing, Plotkin
Week 7
5.1 Linear Codes, generator matrix, the dual, Gilbert-Varshamov, self-dual codes
5.2 The weight distribution of a code, MacWilliams identity
Week 8
5.3 MDS codes
6.1 Hamming and Golay codes
6.2 Reed Muller codes
Week 9
7.1 Finite fields
7.2 Irreducible polynomials
7.3 Roots of unity
Week 10
7.4 Cyclic codes
Week 11
8.1 BCH codes
8.2 Reed-Solomon codes
Week 12
Basic Geometry over a finite field
Week 13
Codes from Geometry
Week 14
Student Presentations
Week 15
Classification of optimal linear codes by computer

Topics for Student Projects:

1. Noisless Coding: Entropy, variable length coding, Kraft, McMillan, Huffman
2. Noisy Coding: Channel, capacity, noisy coding theorem.
3. Goppa codes.
4. Software projects.

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File translated from T_EX by T_THgold, version 4.00.
On 13 Jan 2012, 13:58.