**The Database of Z4 Codes **

Check out the new Database for Z4 Codes

My primary area of research is Algebraic Coding Theory. I received my PhD
from The Ohio State University.

Here is the abstract of my
PhD thesis from OSU web site.

My PhD advisor was Prof.
Dijen Ray-Chaudhuri , the letter "C" in BCH codes refers to him.

Here are some coding
theorists

My areas of interest are:

- Quasi-Cyclic (QC) and Quasi-Twisted (QT) Codes over finite fields and construction of linear codes with improved parameters.
- Codes over Z_4 and construction of good binary (linear or nonlinear) codes.
- Codes over more general rings
- Algebraic or combinatorial constructions of codes with good parameters
- Cryptography
- History of Mathematics and Science, especially in the Islamic World
- Relationship between religion and science
- Mathematics Education/Pedagogy
- Theoretical Computer Science

Publications

Algebraic Coding Theory

·
N. Aydin, A. Halilovic, “ A Generalization of Quasi-twisted Codes: Multi-twisted codes”*, Finite Fields and Their Applications, 45 (2017), 96-106, DOI: http://dx.doi.org/10.1016/j.ffa.2016.12.002*

·
M. Shi, L. Qian, L. Sok, N. Aydin, P. Sole“ On constacyclic codes over Z4[u]/<u^2-1>”, *Finite Fields and Their Applications, 45 (2017), 86–95, DOI: http://dx.doi.org/10.1016/j.ffa.2016.11.016*

· N. Aydin, N. Connolly*, and M. Grassl,“Some results on the structure of constacyclic codes and new linear codes over GF(7) from quasi-twisted codes”, Advances in Mathematics of Communication, Vol 11(1), 2017, 245-258, DOI: 10.3934/amc.2017016

·
M. Ozen, T. Ozzaim, N. Aydin, “ Cyclic codes over Z4 + uZ4 + u^2Z4” to appear in *Turkish Journal of Mathematics.*

·
T. Abualrub, N. Aydin,“Additive Cyclic Codes over Mixed Alphabets and the Football Pool Problem”*, Discrete Math. Algorithm. Appl.* **09**, 1750010 (2017) [13 pages] DOI: http://dx.doi.org/10.1142/S1793830917500100

·
N. Aydin, N. Connolly*, and J. Murphree*,“New binary linear codes from QC codes and an augmentation algorithm” to appear in *Applicable Algebra in Engineering Communication and Computing*.

·
N. Aydin, "Computer algebra challenges for constructing skew cyclic codes", to appear in *Applicable Algebra in Engineering Communication and Computing*.

· N. Aydin, and T.Abualrub. “Optimal quantum codes from additive skew cyclic codes”, Discrete Mathematics, Algorithms, and Applications, 8(1), 2016 DOI:10.10.1142/S1793830916500373.

· M. Ozen, F. Z. Uzekmek, N, Aydin, N. T. Ozzaim, “Cyclic and some constacylic codes over the ring Z4[u]/<u^2-1> ”, Finite Fields and Their Applications, Vol 38, 2016, 27-39.

· R. K. Bandi, M. Bhaintwal, and N. Aydin. “A mass formula for negacyclic codes of length 2^k and some good negacyclic codes over Z4+uZ4”, Cryptography and Communications, 2016, DOI: 10.1007/s12095-015-0172-3.

· E. Chen and N. Aydin, "A database of linear codes over F13 with minimum distance bounds and new quasi-twisted codes from a heuristic search algorithm", JACODESMATH (Journal of Algebra, Combinatorics, Discrete Structures and Applications), Vol 2 (1), 2015,1-16.

· E. Chen and N. Aydin, "New quasi-twisted codes over F11-minimum distance bounds and a new database", J. of Information and Optimization Sciences, Vol 36 (1-2), 2015,129-157.

·
B. Yildiz and N. Aydin,

·
N. Aydin, J. Murphree*

·
S. Karadeniz, B. Yildiz and N. Aydin,

·
T. Abualrub, I. Siap and N. Aydin,

·
N. Aydin, S. Karadeniz, and B. Yildiz,

·
T. Abualrub, N. Aydin, and P. Seneviratne,

·
I. Siap, T. Abualrub, N. Aydin, and P. Seneviratne,

·
I. Siap, T. Abualrub and N. Aydin

·
N. Aydin, and T. A. Gulliver,

·
R. Ackerman*, and N. Aydin,

·
T. Abualrub, A. Ghrayeb,

·
N. Aydin, T. Asamov*,

·

· 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.

·
*Proceedings of International Symposium on
Information Theory* (ISIT 2007), June 24-29 2007, Nice, France, 856-860.

·
T. Asamov*,
and N. Aydin, “LDPC codes
of arbitrary girth”, In *Proceedings of the 10 ^{th} Canadian Workshop on
Information Theory *(CWIT 2007), June 6-8 2007, Edmonton, Alberta, Canada, 69-72.

·
N. Aydin and D. Ray-Chaudhuri “On some
classes of optimal and near-optimal polynomial codes”, Finite Fields and Their Applications*.** *Vol.
**10**, No. 1, pp. 24-35,
January 2004.

· N. Aydin and I. Siap “New quasi-cyclic codes over F5” Applied Mathematics Letters, Vol 15, No 7, pp 833-836, October 2002

·
N. Aydin and D. Ray-Chaudhuri “Quasi-cyclic codes over Z4 and some new binary codes” IEEE Transactions on Information Theory** **Vol.
48, No. 7, pp. 2065-2069, July 2002.

·
N. Aydin, **, **Vol.
23, No. 3, pp. 313-326, December 2001**.**

·
I. Siap, N. Aydin and D. Ray-Chaudhuri “New
1-generator quasi-twisted codes over GF(5)” In *Codes*** ***and Association Schemes*** ***(**Piscataway, NJ, 1999**)**,*
pp. 265-275, DIMACS Ser.
Discrete Math. & Theor. Comp. Sci., *AMS.,
*

· I. Siap, N. Aydin and D. Ray-Chaudhuri “New ternary quasi-cyclic codes with improved minimum distances”,IEEE Transaction on Information Theory, Vol. 46, No. 4, pp. 1554-1558, July 2000.

* denotes a Kenyon undergraduate

History of Science

• N. Aydin and L. Hammoudi, "Root Extraction by Al-Kashi and Stevin", Archive for History of Exact Sciences, Vol 69 (3), pp 291-310, May 2015. DOI 10.1007/s00407-015-0150-3

• Algebra, in *The Oxford Encyclopedia of Philosophy, Science, and Technology in Islam*, May 2014.

• Geometry, in *The Oxford Encyclopedia of Philosophy, Science, and Technology in Islam,* May 2014.

• N. Aydin and M.Rihtim “A striking example of connections between Renaissance Europe and the Muslim World: Copernicus and Tusi” Proceedings of the international conference devoted to the 810th years of Nasireddin Tousi, June 2011, Baku-Azerbaijan, pp. 53-64, National Academy of Sciences of Azerbaijan.

Computer Science

• N. Aydin and P. A. Sivilotti “Remote Belief: Preserving Volition for Loosely-Coupled Processes”, in proceedings of ICDCS 2003, 23 rd International Conference on Distributed Computing Systems, Providence, Rhode Island, pp. 434-440, May 19-22, 2003

Pedagogy/Mathematics Education

• N. Aydin “Enhancing Undergraduate Curriculum via Coding Theory and Cryptography”, PRIMUS (Problems, Resources and Issues in mathematic undergraduate studies) Volume 19 Issue 3, 296-309, May 2009.

• A. S. Ozdemir, E. Guler, N. Aydin, “Effects of Cryptographic Activities on Understanding Modular Arithmetic”, Turkish Journal of Computer and Mathematics Education, Vol.2 No.3, 247-256, 2011.

• N. Aydin and E. Halat “The impacts of undergraduate mathematics courses on college students' geometric reasoning stages”, Montana Mathematics Enthusiasts, Vol 6, Nos 1&2, 151-164, 2009.

• E. Halat, E. Jakubowski E. and N. Aydin “Reform-Based Curriculum and Motivation in Geometry”, Eurasia Journal of Mathematics, Science and Technology Education, Vol 4, No 3, 285-292, 2008.

• N. Aydin “Elliptic Curve Cryptography”, A Computational Science Module developed as part of an NSF grant. December 2011.

• N. Aydin “Public Key Cryptography and the RSA Cryptosystem”, A Computational Science Module developed as part of an NSF grant. July 2009.

• N. Aydin “An Introduction to Coding Theory via Hamming Codes”, A Computational Science Module developed as part of an NSF grant. August 2007.

Presentations

·
“The Legacy of Islamic Math and Science: A Few Examples”, Oberlin College, Oberlin, OH,

·
“The Legacy of Islamic Math and Science: A Few Examples”, University of Michigan-Dearborn, Dearborn, MI,

· “Computer Algebra Challenges for Constructing Skew Cyclic Codes”, ACA (Applications of Computer Algebra) 2014, Fordham University, NY, July 2014.

· “New Databases of Linear Codes over GF(11) and GF(13)”, Karatekin Mathematics Days, at Cankiri Karatekin University, Turkey, June 2014.

·
“The Legacy of Islamic Science in the Modern World: A Few Examples”, Rockford University, Rockford, IL,

· “A History of Mathematics Course for the Liberal Arts”, MAA-Ohio Section Spring 2014 meeting, University of Toledo, Toledo, OH, April 2014.

·
“Islam & Science: The Legacy of Islamic Science in the Modern World”, Noor Islamic Cultural and Community Center

·
“Islam, History and Mathematical Sciences”, Online lecture,

·
“Recent Results in Skew Cyclic Codes”, 31st Ohio State-Denison Mathematics Conference,

·
“Skew Additive Cyclic Codes", ICAAA 2011, International Conference on Applied Analysis and Algebra,

· “A Striking Example to Connections Between Europe and the Muslim World: Copernicus and Tusi” International conference on the history, philosophy of science and technology devoted to the 810-th anniversary of Nasireddin Tousi, June 2011, Baku, Azerbaijan

·
“A Database of Z4 Codes”, The first Int. Conference on Mathematics and
Statistics,

·
“A Perfect Introduction to Coding Theory and Search for Good Codes”, Oberlin College, Oberlin, OH,

·
“Search for Good Linear Codes over Z_4 and
a New Database”, International Conference on Algebra and its
Applications,

·
“Search for Good Linear Codes”, 29th
OSU-Denison Conference, Special Session in Combinatorics, The

·
“Some open problems on quasi-twisted and
related code constructions and good quaternary codes”, International
Symposium on Information Theory,

·
“Enhancing undergraduate mathematics
curriculum via coding theory and cryptography”, Poster presentation, in 3^{rd}
International Conference on the Teaching of Mathematics at the Undergraduate
Level, Istanbul, Turkey, July 2006.

· “Enhancing undergraduate mathematics curriculum via coding theory and cryptography”, MAA Spring 06 meeting, in Ohio Project Next Section, University of Akron, Akron, OH, March 2006.

·
“Affine Cyclic Codes”, AMS Sectional
Meeting,

· “Some generalizations of cyclic codes: Consta-cyclic, quasi-cyclic and quasi-twisted codes”, lecture given in IMA Summer School, at University of Notre Dame, South Bend, IN, June 2004.

· “A Generalization of Quasi-cyclic Codes”, AMS Sectional Meeting, Special Session in Algebraic Coding Theory, Ohio University, Athens, OH, March 2004.

·
“On a Few Classes
of Optimal and Near-Optimal Polynomial Codes”, MTNS 2002,

· “A Class of Near Optimal Polynomial Codes”, Joint Mathematics Meetings, AMS Special Session in Algebraic Coding Theory, San Diego, CA. January 2002.

·
“A Family Polynomial Codes and a Class of
Griesmer Codes”, AMS Sectional Meeting, Special Session in Codes and
Designs, The

· “The Structure of 1-Generator Quasi-Twisted Codes and New Linear Codes” XVth OSU-Dennison Conference, Special Session in Combinatorics, The Ohio-State University, OH, May 2000.

·
“Quaternary Quasi-Cyclic Codes and Some New
Binary Codes”

·
“New Ternary Quasi-Cyclic Codes with
Improved Minimum Distances” AMS Sectional
Meeting,