The Database of Z4 Codes

Check out the 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.
My areas of interest include:

• Algebraic and combinatorial constructions of codes with good parameters over finite fields and rings
• Cyclic codes and their generalizations
• Codes over Z_4 and more general rings
• Code-based cryptography
• Cryptography
• History of Mathematics and Science, especially in the Islamic World. Listen to my story here.
• Relationship between religion and science
• Mathematics Education/Pedagogy
• Theoretical Computer Science

Publications

Books

Miftah al-Hisab, Volume III: Algebra, Translation and Commentary, Springer/Birkhäuser, 2022 (joint work with L. Hammoudi and G. Bakbouk), ISBN 978-3-030-96614-0

Miftah al-Hisab, Volume II: Geometry, Translation and Commentary, Springer/Birkhäuser, 2020 (joint work with L. Hammoudi and G. Bakbouk), ISBN 978-3-030-61329-7

Miftah al-Hisab, Volume I: Arithmetic, Translation and Commentary, Springer/Birkhäuser, 2019 (joint work with L. Hammoudi), ISBN 978-3-030-14949-9

Algebraic Coding Theory and Cryptography 

· H. Ou-azzou, M. Najmeddine, N. Aydin, On isometry and equivalence of skew constacyclic codes, Discrete Mathematics, 2025, https://doi.org/10.1016/j.disc.2024.114279

· N. Aydin, Y. Cengellenmis, A. Dertli, Cyclic and Constacyclic codes over Z4 + wZ4, accepted for publication in Bulletin of the Korean Mathematical Society, 2024.

· H. Ou-azzou, M. Najmeddine, N. Aydin, P. Liu*, B. Ialou, E. M. Mouloua, Linear codes invariant under a linear endomorphism, accepted for publication in Advances in Mathematics of Communication, 2024.

· H. Ou-azzou, M. Najmeddine, N. Aydin, On the algebraic structure of quasi-polycyclic codes and new quantum codes, Quantum Information Processing, 23(3),2024.

· T. Abualrub, S. Karbaski, N. Aydin and P. Liu*. Additive polycyclic codes over F4 induced by nonbinary polynomials, Journal of Applied Mathematics and Computing, 2023.

·  S. R. Pandey*, N. Aydin, E. Z. Chen, F. Jönsson, K. Klonowska, New Results and Bounds on Codes over GF(19), accepted for publication in J. Information and Optimization Sciences, 2024.

·H. Ou-azzou, M. Najmeddine, N. Aydin, E. M. Mouloua, On the algebraic structure of (M,sigma,delta)-skew codes, accepted for publication in Journal of Algebra, 2023.

· H. Ou-azzou, M. Najmeddine, N. Aydin. Linear codes invariant under cyclic endomorphisms, accepted for publication in Journal of Algebra and Its Applications, 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, T.Guidotti*, P. Liu*,  Good classical and quantum codes from multi-twisted codes,  Contemporary Mathematics, Algebra and Coding Theory, 785:7 2023, https://doi.org/10.1090/conm/785/15771

·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

· B. Caliskan, N. Aydin, P. Liu*, Skew cyclic codes over Z4+uZ4+vZ4,  Cryptogr. Commun., Vol 15, 845-858, (2023), https://doi.org/10.1007/s12095-023-00645-3

· F. Caliskan, R. Aksoy, N. Aydin, P. Liu*, Entanglement-Assisted Binary Quantum Codes from Skew Cyclic Codes over F_2 x (F_2+vF_2), accepted for publication in Quantum Information Processing.

· E. Z. Chen, N. Aydin, F. Jönsson, K. Klonowska, New Results and Bounds on codes over GF(17), JACODESMATH, 11(1), 2024, 27-39

· Z. Hebbache, A. Kaya, N. Aydin, K. Guenda, On Some Skew Codes over Zq+uZq, Discrete Mathematics, Algorithms, and Applications, 16(01), 2250186 (2024),https://doi.org/10.1142/S1793830922501865

· D. Akre*, N. Aydin, M. Harrington*, S. Pandey*, A Generalization of  Cyclic  Code Equivalence Algorithm to Constacyclic Codes,  Des. Codes Cryptogr. 91, 763–777 (2023). https://doi.org/10.1007/s10623-022-01124-1 

·D. Akre*, N. Aydin, M. Harrington*, S. Pandey*, New Binary and Ternary Quasi-Cyclic Codes with Good Properties,  Comp. Appl. Math. 42, 102 (2023). https://doi.org/10.1007/s40314-022-01946-8

·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, 2023,  649–661. https://doi.org/10.1007/, arxiv version  

· A. Dertli, Y. Cengellenmis, and N. Aydin, On Skew Cyclic Codes over a mixed alphabet and their applications to DNA codes, Discrete Mathematics, Algorithms and Applications, 2021, https://doi.org/10.1142/S1793830921501433

· N. Aydin, B. Yildiz, and S. Uludag,A Class of Weak Keys for the QC-MDPC Cryptosystem, 2020 Algebraic and Combinatorial Coding Theory (ACCT), Albena, Bulgaria, 2020, pp. 1-4, doi: 10.1109/ACCT51235.2020.9383383.

· N. Aydin, T. Guidotti*, and P. Liu*,New Linear Codes as Quasi-Twisted Codes from Long Constacyclic Code,  2020 Algebraic and Combinatorial Coding Theory (ACCT), Albena, Bulgaria, 2020, pp. 1-6, doi: 10.1109/ACCT51235.2020.9383237.

· N. Benbelkacem, M. F. Ezerman, T. Abualrub, N. Aydin and A. Batoul, Skew Cyclic Codes Over F_4 R, Journal of Algebra and Its Applications. 2250065, (2022), DOI: 10.1142/S0219498822500657

·Y. Cengellenmis, N. Aydin, A. Dertli,Reversible DNA Codes from Skew Cyclic Codes over a Ring of Order 256, Journal of Algebra Combinatorics Discrete Structures and Applications, Vol 8(1), 1-8, 2021.

· T. Abualrub, N. Aydin, I. Aydogdu, Optimal Binary Codes Derived from F2F4-additive Cyclic Codes, Journal of Applied Mathematics and Computing, 64,71–87 (2020). https://doi.org/10.1007/s12190-020-01344-5

· 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.

· A. Melakhessou, N. Aydin, Z. Hebbache,K. Guenda, Zq(Zq+uZq)-linear skew constacyclic codes, Journal of Algebra Combinatorics Discrete Structures and Applications, 17(1), 2020, 85-101.

· N. Aydin,Y. Cengellenmis, A. Dertli,S. T. Dougherty, E. Salturk  Skew cyclic and skew constacyclic codes over the local Frobenius non-chain rings of order 16, Advances in Mathematics of Communication, 14(1), Feb 2020, 53-67.

· N. Aydin, “Some new linear codes from skew cyclic codes and computer algebra challenges”, Applicable Algebra in Engineering Communication and Computing, March 2019, https://doi.org/10.1007/s00200-019-00383-1

· 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,G. Bakbouk*, J. Lambrinos*, “New Linear Codes over non-Prime Fields”, Cryptography and Communications, 11(5), 891-902, 2019, DOI: 10.1007/s12095-018-0333-2

· 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. 

· M. Ozen, F. Z. Uzekmek, N, Aydin, N. T. Ozzaim, “One generator quasi-cyclic codes over F2+v ”, J. Appl Math & Informatics, Vol 36, 2018, 359-378, https://doi.org/10.14317/jami.2018.359  

· Y. Cengellenmis, A. Dertli, N. Aydin, “Some constacyclic codes over Z4[ u]/ < u^2>, new Gray maps, and new quaternary cod”, Algebra Colloquim, 25(3), 2018, 369-376

· R. Dastbasteh, H. Mousavi, T. Abualrub, N. Aydin, J. Haghighat, “Skew cyclic codes over F_p+uF”, Int. J. of Information and Coding Theory, Vol 5. No. 1, 2018, 81--99.

· N. Aydin, A. Dertli, Y. Cengellenmis, “On some constacyclic codes over  Z4[ u]/ < u^2-1>, their Z4 images, and new codes”, Des. Codes Cryptogr. 86(6), 2018, :1249–1255, DOI: 10.1007/s10623-017-0392-y

· M. Ozen, T. Ozzaim, N. Aydin, “Cyclic codes over Z4 + uZ4 + u^2”, Turkish J. Math. 41(5), 2017, 1235-1247, DOI: 10.3906/mat-1602-35

· A. Batoul, K. Guenda, T. A. Gulliver, N. Aydin, “Constacyclic codes over finite principal ideal rin” International Conference on Codes, Cryptology, and Information Security C2SI 2017, Springer LNCS 10194, pp 161-175, DOI 10.1007/978-3-319-55589-8_11

· A. Batoul, K. Guenda, T. A. Gulliver, N. Aydin, “On isodual cyclic  codes over finite chain rings” International Conference on Codes, Cryptology, and Information Security C2SI 2017, Springer LNCS 10194, pp 176-194, DOI 10.1007/978-3-319-55589-8_12.

· N. Aydin, N. Connolly*, J. Murphree* “New binary linear codes from QC codes and an augmentation algorithm”AAEC. 28(4) 339-350, August 2017, DOI https://doi.org/10.1007/s00200-017-0327-x

·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

· 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, 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, https://doi.org/10.1016/j.ffa.2015.12.003

· 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, “ On Cyclic codes over Z_4+uZ4 and their Z4-images”, International Journal of Information and Coding Theory, Vol 2 (4), 2014, 226-237.

·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", FILOMAT, Vol 28 (5), 2014, 937-945.

· 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 (1), 2011, 10-20.

·  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 dual” 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 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, I. Siap and D. Ray-Chaudhuri “The structure of 1-generator quasi-twisted codes and new linear codes”,Designs Codes and Cryptography, Vol. 24, 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

• N. Aydin, "The Legacy of Islamic/Arabic Mathematics", MAA Focus, April/May 2024.

• N. Aydin, "The Role of Religion in the Development of Mathematical Sciences in Medieval Islamic Civilization", Muslim Heritage, 2021.

• 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, “Impacts of a unique course on the history of mathematics in the Islamic World”, MAA Convergence, July 2017

• 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 “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.

•  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.

Conference Presentations

·        "Coding Theory: Past, Present, and Future", Invited Talk, International Urdu Science Conference, MANUU, Hyderabad, India, March 2024.

·        "Coding Theory as Pure and Applied Mathematics: Its Connections and Applications", Invited Keynote Speech, ICDMC-2023, Bengaluru India, 20 December 2023.

·        "Pure Math, Applied Math, Information Theory and the Place of Algebra in Mathematics", Invited Talk (virtual),First IIIMT-Algebra Forum Conference, 16 December 2023.

·        "An Updated Database of Z4 codes and an Open Problem About QC codes", Codes, Cryptology, and Information Security, C2S1-2023, May 2023, (N.Aydin, Y. Lu*, V. Onta*)

·        “ On Some Special Matrices and Their Application to Code Construction”, ALCOCRYPT 2023, Marseille, France, February 2023 (presented by K. Guenda) ” .

·        “The Additive polycyclic codes over F4 II: The general case”, ALCOCRYPT 2023, Marseille, France, February 2023 (presented by T. Abualrub) ” .

·        “The Need for Teaching a More Accurate and Inclusive History of Mathematics and Science ”, Leiden University, March 2023.

·        “The Need for Teaching a More Accurate and Inclusive History of Mathematics and Science ”, MAA MathFest, August 2022 (presented in the session Pursuing Justice in and through Mathematics)

·        “Algebraic Coding Theory and Code-Based Cryptography”, MAA MathFest, August 2022 (presented in the session Coding Theory and its Applications)

·        “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, 2020, April 2022 (N. Aydin*, D. Akre, M. Harrington, and S. Pandey).

·        “The Need for Including Islamic Math and Science in School Curricula", Joint Mathematics Meetings, 2020, April 2022.

·        “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).

·        “ Al-Kashi's Miftah al-Hisab: a 21st century translation and reading”, Joint Mathematics Meetings 2020, in AMS Special Session on Current Areas of Interest in the Mathematical Sciences of Medieval Islam, Denver, CO, USA January 2020 (N. Aydin and L. Hammodi*).

·        “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, and R. O. VandenBerg*).

·        “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*)

·        “Code-Based Crytography for the Internet-of-Things", 4 hour tutorial in IEEE Consumer Communications & Networking Conference, Las Vegas, NV, January 2019 (N. Aydin, S. Uludag, and B. Yildiz).

·        “A Generalization of Quasi-Twisted Codes: Muti-twisted Codes", AMS Sectional Meeting (#1136), The Ohio StateUniversity, Columbus, OH, March 2018.

·        “ Translation of Miftah al-Hisab", Midwest History of Math Conference and ORESME Joint Meeting, Wabash College, Crawfordsville, IN, Sep 2017.

·        “ Recent Methods of Constructing New Linear Codes over Z4”, Mathematical Congress of the Americas, in Special Session on Finite Algebraic Combinatorics and Applications, Montreal, Canada, July 2017.

·        “ Legacy of Al-Kashi: Why does it matter in the 21st century”, Joint Mathematics Meetings 2016, in AMS Special Session on Current Areas of Interest in the Mathematical Sciences of Medieval Islam, Seattle, WA, USA January 2016 (N. Aydin*, and L. Hammoudi)

·        “ New Binary Linear Codes from Quasi-Cyclic Codes and an Augmentation Algorithm", The International Conference on Coding Theory and Cryptography (ICCC 2015), USTHB, Algiers, Algeria, November 2015.

·        “ The Legacy of Islamic Science in the Modern World: A Few Examples”, Grand Dialogue in Religion & Science, Grand Valley State University, Grand Rapids, MI, June 2015.

·        “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.

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

·        “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.

·        “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 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, University of Pittsburgh, Pittsburgh, PA November 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.

Other Presentations

·        Delivered several talks on “Coding Theory” and “The Legacy of Islamic Math and Science” in various places in India in December 2023.

·        Numerous invited talks on “Coding Theory” and “The Legacy of Islamic Math and Science” in various places in Algeria and Morocco during my Fulbright stay in the AY 2022-23.

·        "Lessons from House of Wisdom and a Vision for Future", A Revival of Islamic Academia Conference Memphis, TN, July 2023

·        "Search for Good Linear Codes: The ASR Algorithm and Its Generalizations", invited talk (remote), Algebra with Applications Seminar, Aligarh Muslim University, India, May 2023.

·        “An Upper Level Math Course in Coding Theory and Cryptography", Crypto Educators Seminar, virtual, April, 2023 (recording available) .

·        “A Mathematician's Journey into History of Mathematics: Impacts, Reflections, and Lessons", invited national talk, MAA Special Interest Group on History of Mathematics (HOM SIGMAA), November 3, 2021 (recording available from the presenter).

·        “Islamic Art and Geometric Designs of Mosques", presentation in the workshop titled Exploring the Sacred in the Islamic Tradition organized by Spirituality Network, Columbus, OH November, 2019

·        "Research in  Coding Theory: An Efficient Way to Mathematical Fame and a Promise for the Quantum Age", Colloquim Talk, New College of Florida, Sarasota, FL, March 2019.

·        “ The Legacy of Islamic Math and Science: Why does it Matter in the 21st Century?", Colloquim Talk, New College of Florida, Sarasota, FL, March 2019.

·        “ The Legacy of Islamic Math and Science: Why does it Matter in the 21st Century?", Mathematics Colloquim, Northern Arizona University, Flagstaff, AZ, March 2018.

·        “Recent Results in Quasi-Twisted and Related Codes, and Codes over Rings", ACGT Seminar, Northern Arizona University, Flagstaff, AZ, March 2018.

·        “Teaching a More Accurate and Inclusive History of Science", (poster) Franklin University Scholars Showcase, Columbus, OH, October 2018.

·        “The Legacy of Islamic Math and Science: A Few Examples”, Oberlin College, Oberlin, OH, March 4, 2015.

·        “The Legacy of Islamic Math and Science: A Few Examples”, University of Michigan-Dearborn, Dearborn, MI, March 3, 2015.

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

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

·        “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.