There are many problems and projects in Algebraic Coding Theory that are accessible to undergraduates. In general, we combine algebraic theory with programming skills to search for new codes, codes with better parameters than currently best known codes. This is one of the main problems of coding theory. One of the interesting feature of the problem is that it can be approached from many different perspectives using many different tools, some very sophisticated (e.g. advanced algebraic geometry), some rather elementary (e.g. elemenatry but insightful search algorithms). If you are interested in doing research in this area please do not hesitate to contact me. Below is a list of undergradute projects, papers and presentations produced by Kenyon students. Minimal background needed to get started is a course on Linear Algebra. Additionally, courses on computer programming, Abstract Algebra and Combinatorics are highly recommended.
Kenyon Summer Science Scholars Projects
- Nick Connolly'15: Constructing New Linear Codes with Record Breaking Parameters over GF(7), Summer 2014.
- John Murphree'15: New Linear Codes from Constacyclic codes, Summer 2013.
- Ryan Ackerman'10: Quasi-twisted codes over GF(5), Summer 2009.
- Tsvetan Asamov '08: Low Density Parity Check Codes II, Summer 2006
- Tsvetan Asamov '08: Methods of Constructions for Low Density Parity Check Codes, Summer 2005
- Irina Ivan '08: Low Density Parity Check Codes, Summer 2005
- Ben Johnson '06: Multitwisted Codes, Summer 2004
Publications with Kenyon Undergraduates
J. Murphree*, “New linear codes from constacyclic codes”,Journal of the Franklin Institute, Vol 351 (3), March 2014, 1691-1699
R. Ackerman* , and N. Aydin,
“New quinary linear codes from quasi-twisted codes and their duals”
Applied Mathematics Letters, Vol 24, No 4, pp 512-515, April 2011.
Search for good linear codes in the
class of quasi-cyclic and related codes ” Selected Topics in Information and Coding Theory", Edited Book, I. Woungang, S. Misra, S. Chandra Misra
(Eds.), Series on Coding and Cryptology, World Scientific Publishing, ISBN:978-981-283-716-5/981-283-716-7,
March 2010, 724 pages
T. Asamov*, “A Database of Z4 Codes”, J. of Combinatorics, Information & System Sciences (JCISS), Vol. 34 No. 1-4 Comb, 2009, p: 1-12.
and N. Aydin. “A search algorithm for linear codes: progressive
dimension growth”, Designs, Codes and Cryptography, Vol. 45, No 2, pp. 213-217, November 2007.
N Aydin, T. Asamov*, and T. A. Gulliver “Some
open problems on quasi-twisted and related code constructions and good
quaternary codes”, In Proceedings of International Symposium on
Information Theory (ISIT 2007), June 24-29 2007, Nice, France, 856-860.
and N. Aydin, “LDPC codes
of arbitrary girth”, In Proceedings of the 10th Canadian Workshop on
Information Theory (CWIT 2007), June 6-8 2007, Edmonton, Alberta, Canada, 69-72.
* denotes a Kenyon undergraduate
Conference Presentations by Kenyon Students (or presentations of joint work by Professor Aydin)
"Constructing New Linear Codes with Record Breaking Parameters", by N. Connolly, MAA MathFest, Portland, Oregon,, August 2014.
"New Linear Codes from Constacyclic codes", poster presentation by J. Murphree, Young Mathematicians Conference, The Ohio State University, August 2013
"A Database of Z4 Codes", by N. Aydin (contributions by T. Asamov), The first Int. Conference on Mathematics and Statistics, American University of Sharjah, Sharjah, UAE. March 2010.
"Some open problems on quasi-twisted and related code constructions and good quaternary codes”, by N. Aydin (contributions by T. Asamov), International Symposium on Information Theory, Nice, France, June 2007.
"LDPC Codes of Arbitrary Girth”, by T. Asamov, AMS Special Session on Algebraic Coding Theory, U of Cincinnati, September 2006.
"Search for New Error Correcting Codes" by B. Johnson, Young Mathematicians Conference, The Ohio State University, August 2004.