WEEK |
DATES |
ASSIGNMENTS |
SECTION/BOOK |
TOPICS |
~ |
Sep. 10-11 |
~ |
~ |
Introduction to the course. What is coding theory. Basics of finite fields. |
1 |
Sep. 14-18 |
~ |
LN 8.1 |
Linear codes. Symmetric and Gaussian channels. Capacity. |
2 |
Sep. 21-25 |
~ |
LN 8.1 |
Decoding linear codes. Bounds. |
3 |
Sep. 28 - Oct 2 |
A1 out: Sep. 29 |
LN 8.2; MS 3.1; MS 3.3 |
2-error-correcting BCH codes. Finite fields. Polynomials. |
4 |
Oct. 5-9 |
~ |
LN 1.2-1.4 |
Review: rings, fields and ideals.
Extension fields. Splitting fields. |
5 |
Oct. 12-16 |
~ |
LN 2.1 |
Characterization of finite fields. |
6 |
Oct. 19-23 |
A1 in / A2 out: Oct. 20 |
LN 2.2-2.3; LN 2.5 |
Characterization of finite fields (cont). |
7 |
Oct. 26-30 |
Midterm test |
McE 5 |
Primitive elements and Gauss algorithm. |
8 |
Nov. 2-6 |
~ |
LN 3.2; vzGG 14.9 |
Number of irreducible polynomials.
Finding irreducible polynomials. |
9 |
Nov. 9-13 |
A2 in / A3 out: Nov. 10 |
vzGG 14.1-14.6 |
Squarefree, distinct-degree and equal-degree
factorization. |
10 |
Nov. 16-20 |
~ |
MS 7; vzGG 14.10 |
Cyclic codes. Generator polynomial. |
11 |
Nov. 23-27 |
~ |
MS 7 |
BCH codes revisited. Computing minimal polynomials.
|
12 |
Nov. 30 - Dec. 4 |
A3 in: Dec. 1 |
MS 10; HHLLPRW 6 |
Reed-Solomon codes. Review of course.
Comments on final exam. |
vzGG is ``Modern Computer Algebra'', by J. von zur Gathen and
J. Gerhard, 2nd edition, Cambridge University Press, 2003.
HHLLPRW is ``Coding Theory and Cryptography: the Essentials'',
by D.R. Hankerson, D.G Hoffman, D.A. Leonard, C.C. Lindner, K.T. Phelps,
C.A. Rodger and J.R. Wall, Marcel Dekker Inc., 2000.
LN is ``Introduction to Finite Fields and Their Applications'',
by R. Lidl and H. Niederreiter, Cambridge University Press, 1994.
MS is ``The Theory od Error-Correcting Codes'', by
F.J. MacWilliams and N.J.A. Sloane, North-Holland, Elsevier Science, 1977.
McE is ``Finite Fields for Computer Scientists and Engineers'',
by R. McEliece, Kluwer Academic Press, 1987.