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
  • Mathematics Education/Pedagogy
  • Theoretical Computer Science

Publications

Algebraic Coding Theory

·        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", accepted for publication in JACODESMATH (Journal of Algebra, Combinatorics, Discrete Structures and Applications)

 

·        E. Chen and N. Aydin, "New quasi-twisted codes over F11-minimum distance bounds and a new database", accepted for publication in J. of Information and Optimization Sciences

 

·        B. Yildiz and N. Aydin, “ On Cyclic codes over Z_4+uZ4 and their Z4-images”, accepted for publication in International Journal of Information and Coding Theory.

 

·        N. Aydin, J. Murphree* “New Linear Codes from Constacyclic Codes” Journal of the Franklin Institute, Vol 351 (3), March 2014, 1691-1699.

 

·        S. Karadeniz, B. Yildiz and N. Aydin, “ Extremal binary self-dual codes of lengths  64 and 66  from four circulant constructions over F2+uF2", accepted for publication in FILOMAT.

 

·        T. Abualrub, I. Siap and N. Aydin, “Z_2Z_4-additive cyclic codes”, IEEE Transactions on Information Theory, Vol 60 (3), March 2014, 1508-1514.

 

·        N. Aydin, S. Karadeniz, and B. Yildiz, “Some new binary quasi-cyclic codes from codes over the ring F2 + uF2+vF2+uvF2”, Applicable Algebra in Engineering, Communication and Computing. Vol 24 (5), Nov 2013, 355-367.

 

·        T. Abualrub, N. Aydin, and P. Seneviratne, “Theta-Cyclic Codes Over F2 + vF2”, Australasian Journal of Combinatorics, Vol 54, October 2012, 115-126,

 

·        I. Siap, T. Abualrub, N. Aydin, and P. Seneviratne, “Skew quasi-cyclic codes of arbitrary length” International Journal of Information and Coding Theory, Vol 2, No 1, pp 10-20, 2011.

 

·        I. Siap, T. Abualrub and N. Aydin “Quaternary quasi-cyclic codes with even length components” Ars Combinatoria Vol CI, July 2011 pp. 425-434

 

·        N. Aydin, and T. A. Gulliver, “Some good cyclic and quasi-twisted Z4-linear codes”, Ars Combinatoria, Vol XCIX, Apr 2011, pp. 503-518.

 

·        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.

 

·        T. Abualrub, A. Ghrayeb, N. Aydin , and I. Siap, “On the construction of  skew quasi-cyclic codes” IEEE Transactions on Information Theory, Vol. 56, No. 5, pp. 2081-2090, May 2010.

 

·        N. Aydin, T. Asamov*, “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.

 

·        N. Aydin , and T. Asamov*, “A Database of Z4 Codes”,  J. of Combinatorics, Information & System Sciences (JCISS), Vol. 34 No. 1-4 Comb, 2009, p: 1-12.

 

·        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.

 

·         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.

 

·        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.

 

·        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, I. Siap and D. Ray-Chaudhuri “The structure of 1-generator quasi-twisted codes and new linear codes”,Designs Codes and Cryptography, 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., Providence, RI, 2001.

 

·        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

• 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

·        “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, April 2014.

 

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

 

·        “The Legacy of Islamic Mathematics and Science: A Few Examples”, The College of Wooster, Wooster,November 2013.

 

·        “Islam & Science: The Legacy of Islamic Science in the Modern World”, Noor Islamic Cultural and Community Center , Columbus, OH October 2013.

 

·        “Islam, History and Mathematical Sciences”,  Online lecture, Hast-o-Neest Institute of Traditional Studies & Arts, Pakistan, January 2013.

 

·        “Recent Results in Skew Cyclic Codes”,  31st Ohio State-Denison Mathematics Conference, The Ohio State University , Columbus, OH May 2012.

 

·        “Skew Additive Cyclic Codes",  ICAAA 2011, International Conference on Applied Analysis and Algebra, Yildiz Technical University , Istanbul Turkey, July 2011.

 

·       “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, American University of  Sharjah, Sharjah, UAE. March 2010.

 

·        “A Perfect Introduction to Coding Theory and Search for Good Codes”, Oberlin College, Oberlin, OH, November 2008.

 

·        “Search for Good Linear Codes over Z_4 and a New Database”, International Conference on Algebra and its Applications, Ohio University, Athens, OH, June 2008.

 

·        “Search for Good Linear Codes”, 29th OSU-Denison Conference, Special Session in Combinatorics, The Ohio State University, Columbus, OH, May 2008.

 

·        “Some open problems on quasi-twisted and related code constructions and good quaternary codes”, International Symposium on Information Theory,  Nice, France, June 2007.

 

·        “Enhancing undergraduate mathematics curriculum via coding theory and cryptography”, Poster presentation, in 3rd 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, University of Pittsburgh, Pittsburgh, PA November 2004.

 

·        “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, University of Notre Dame, South Bend, IN, August 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 Ohio State University, Columbus, OH. September 2001.

 

·        “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” AMS Sectional Meeting Notre Dame University, Special Session in Algebraic Coding Theory, South Bend, IN. April 2000.

 

·        “New Ternary Quasi-Cyclic Codes with Improved Minimum Distances” AMS Sectional Meeting, University of Utah, Salt Lake City, UT. September 1999.