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 a variety of tools, some very sophisticated (e.g. advanced algebraic geometry), some rather elementary (e.g. elementary but insightful search algorithms). If you are interested in doing research in this area I encourage you to contact me. Projects are available for beginners and experts. 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 and some programming experience. Additionally, courses on Abstract Algebra, Combinatorics, and advanced programming (e.g. Data Structures) are highly recommended.
In addition to our active undergraduate research program with Kenyon students, I also mentor highly motivated and exceptionally strong international high school students for research in coding theory and cryptography offered by Pioneer Academics. This unique program connects talented high school students from all around the world with resources to conduct research. We have also published papers with Pioneer scholars such as this.
Research Projects with Kenyon Students
Publications with Kenyon Undergraduates
T. Guidotti*, P. Liu*,
and quantum codes from multi-twisted codes, Contemporary
and Coding Theory, 785:7 2023,
· A. Bellil, K. Guenda, N. Aydin, P. Liu*, T. Aaron Gulliver. Constacyclic and quasi-twisted codes over Zq[u]/< u^2-1> and new Z4-linear codes. Advances in Mathematics of Communications, 2023 doi: 10.3934/amc.2023026
· N. Aydin, Y. Lu*, V. Onta*, An updated database of Z4 codes and an Open Problem about Quasi-Cyclic Codes, In: El Hajji, S., Mesnager, S., Souidi, E.M. (eds) Codes, Cryptology and Information Security. C2SI 2023. Lecture Notes in Computer Science, vol 13874. Springer, Cham. https://doi.org/10.1007/978-3-031-33017-9_24
R. Aksoy, N. Aydin, P. Liu*, Entanglement-Assisted
Codes from Skew Cyclic Codes over F_2 x (F_2+vF_2),
Processing, 22, 208 (2023).
N. Aydin, P. Liu*, Skew cyclic codes over Z4+uZ4+vZ4, Cryptography
2023,15 , 845–858, DOI: 10.1007/s12095-023-00645-3
· D. Akre*, N. Aydin, M. Harrington*, S. Pandey*, New Binary and Ternary Quasi-Cyclic Codes with Good Properties, Accepted for publication in Computational and Applied Mathematics, 2022.
· S. Pandey*, N. Aydin, M. Harrington*, D. Akre*, A Generalization of the ASR Search Algorithm to 2-Generator Quasi-Twisted Codes, ISIT 2022.
· N. Aydin, P. Liu*, B. Yoshino*. Polycyclic Codes Associated with Trinomials: Good Codes and Open Question, Designs,Codes, and Cryptography 2022.
· A. S. Karbaski, T. Abualrub, N. Aydin and P. Liu*. Additive Polycyclic Codes over F_4 Induced by Binary Vectors and Some Optimal Codes, Advances in Mathematics of Communications, 2022.
· N. Aydin, P. Liu*, B. Yoshino*. A Database of Quantum Codes, J. of Algebra Combinatorics Discrete Structures and Applications, 2021.
· N. Aydin and O. R. Vandenberg* A New Algorithm for Equivalence of Cyclic Codes and Its Applications, Applicable Algebra In Engineering, Communication and Computing, 2021, DOI 10.1007/s00200-021-00525-
· N. Aydin,T Guidotti*, P.Liu*, New Linear Codes as Quasi-Twisted Codes from Long Constacyclic Codes, 2020 Algebraic and Combinatorial Coding Theory (ACCT), Albena, Bulgaria, 2020, pp. 1-6, doi: 10.1109/ACCT51235.2020.9383237.
· N. Aydin,T Guidotti*, P.Liu*, A Shaikh*, O VandenBerg*, Some Generalizations of the ASR Search Algorithm for Quasi-Twisted Codes, Involve, Vol 13(1), 2020, 137-148.
· N. Aydin, J. Lambrinos*,Oliver VandenBerg*, “On Equivalence of Cyclic Codes, Generalization of a Quasi-Twisted Search Algorithm, and New Linear Codes”, Designs, Codes and Cryptography, 2019, DOI:10.1007/s10623-019-00613-0
· N, Aydin, D. Foret*, “New Linear Codes over GF(3), GF(11), and GF(13) ”, Journal of Algebra Combinatorics Discrete Structures and Applications, 6(1), 13-20, 2019.
· T. Asamov*, 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.
· T. Asamov*, 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, DOI: 10.1109/CWIT.2007.375703
* denotes a Kenyon undergraduate
Conference Presentations by Kenyon Students (or presentations of joint work by Professor Aydin)
· “A Generalization of the ASR Search Algorithm to 2-Generator Quasi-Twisted Codes” ISIT 2022, June 2022 (N. Aydin, D. Akre*, M. Harrington*, and S. Pandey*).
· “A Generalization of the ASR Search Algorithm to 2-Generator Quasi-Twisted Codes” Joint Mathematics Meetings (virtual), April 2022 (N. Aydin, D. Akre*, M. Harrington*, and S. Pandey*).
· “New Binary and Ternary Quasi-Cyclic Codes with Good Properties” Joint Mathematics Meetings (virtual), April 2022 (N. Aydin, D. Akre*, M. Harrington*, and S. Pandey*).
· “New Linear Codes from 2-Generator Quasi-Twisted Codes” Joint Mathematics Meetings (virtual), April 2022 (poster presented by S. Pandey*).
· “Good Codes from Quasi-Cyclic Codes Using ConstructionX” Joint Mathematics Meetings (virtual), April 2022 (poster presented by M. Harrington*).
· “New Linear Codes as QT codes from Long Constacyclic Codes”, ACCT 2020 (17th Int Workshop on Algebraic and Combinatorial Coding Theory), Bulgaria, October 2020 ( N. Aydin, T. Guidotti*, and P. Liu*).
· “A New Algorithm for Equivalence of Cyclic Codes and Its Applications”, AMS Contributed Paper Session on Computer Science, Programming, Information and Related Topics, Joint Mathematics Meetings 2020, in, Denver, CO, USA, January 2020 (N Aydin R. O. VandenBerg*).
· “Generalization of a Linear Code Search Algorithm”, MAA Undergraduate Student Poster Session, Joint Mathematics Meetings 2020, in, Denver, CO, USA, January 2020 (poster presented by R. O. VandenBerg*). Received Honorable Mention.
· “New Results on Equivalence of Cyclic Codes and a Generalization of a Search Algorithm", Southeastern International Conference on Combinatorics, Graph Theory, and Computing, Florida Atlantic University, FL, March 2019. (N. Aydin and R. O. VandenBerg*)
· "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.