9:30-10:45: Error control codes, especially linear block codes
11:00-12:00: Supplemental lecture: Ideals, rings and algebraic varieties
1:45-3:00: Codes with "extra structure:" cyclic and multicyclic codes
3:00-3:30: Tea/cookies, Blocker 156
9:30-10:45: More on structure of finite fields, Reed-Solomon and BCH codes
11:00-12:00: Supplemental lecture: Grobner bases
1:45-3:00: Encoding and decoding algorithms via Groebner bases
3:00-3:30: Tea/cookies, Blocker 156
3:30-5:00: Problem session for students to present solutions to HW problems, Blocker 156
9:30-10:45: Algebraic-geometric Goppa codes and codes from order domains
1:45-3:00: The Berlekamp-Massey-Sakata decoding algorithm
3:00-3:30: Tea/cookies, Blocker 156
3:30-5:00: Problem session for students to present solutions to HW problems, Blocker 156
5:00-7:00: Barbecue dinner, area immediately outside Blocker 156
References:
[1] Huffman, W. Cary, and Pless, Vera, Fundamentals of Error-Correcting
Codes, Cambridge University Press, 2003.
[2] Cox, D., Little, J., and O'Shea, D. Using Algebraic Geometry,
2nd edition, Springer, 2005. (Chapters 9 and 10)
[3] Fitzpatrick, P. "On the key equation," IEEE Trans. Inform.
Theory v. 41 (1995), 1290-1302. (The original source for the Groebner basis formulation
of the decoding algorithms in Lecture 4 above)
[4] Geil, O. and Pellikaan, R. "On the Structure of Order Domains,"
Finite Fields Appl. v. 8 (2002), 369-396.
[5] Little, J.
The Ubiquity of Order Domains for the Construction
of Error Control Codes preprint: arXiv: math.AC/0304292.
(shows how general the order domains in Lecture 5 actually are)
[6] Little, J.
TAGS workshop notes: error control codes from algebra and geometry.