Project Title: Average Covering Radius of Algebraic Codes
Adviser :
Vyacheslav Rykov
Description:
In this project, we will consider several known error-correcting code families for use in a steganography channel. A steganography channel is a method of transmitting hidden data by embedding it into another document in a way that is difficult to detect [2]. Good codes for steganography channels must have minimum value of the average covering radius. It is easy to verify that the average covering radius of a group code may be computed by taking the average weight of the minimum-weight leaders for each group coset. Then the average covering radius can be found by exact calculation of random samples or can be found by using the weight distribution of the code. We will try to find the average covering radii of known error-correcting codes.
In this project we propose that the participating student engages in
the following activities:
A. Study the theoretical aspects of the problem by using following sources:
1. G. Cohen, I. Honkala,
S. Litsyn, A. Lobstein,
“Covering Codes”,
2. F. Galand, G. Kabatiansky, “Information Hiding by Coverings", Proc. of IEEE Information Theory Workshop, 2003, pp. 151-154.
3. F.J. MacWilliams, N.J.A. Sloan, “The
Theory of Error-Correcting Codes”,
4. A.G. Dyachkov , D.M. Harnett, V.V. Rykov, “On
Error-Correcting Codes for a Steganography Channel”,
2007, be published
This will help her/him understand the research topic and serve as an introduction to the final, written, research report.
B. Develop algorithms for finding the average covering radii.
C . Write computer programs for the average covering radii calculations.
D. Run the programs and help the adviser in analyses of the covering properties of codes.
E. Put together her/his findings, written software, significant graphs, tables, and so on in the final research report to be presented at the MAM Symposium.
OTHER REQUIREMENTS: The students interested in the project above are expected to have taken and passed with maximal grades or close MATH 1950(Calc I), MATH 1960(Calc II), MATH 4050 (Linear Algebra) and MATH 4030 (Applied Modern Algebra). They should be familiar with computers and MAPLE, and be willing to learn GAP computer algebra system. The student is also expected to meet with the adviser a couple of times a week, (or communicate actively by e-mail) for discussions, guidance, and progress reports during the preparation period of the project.